Intermediate advice

As usual, I see guides explaining the basics, including the combat guide explaining how the rules work, but I don't see anything past basics.
Let's fix this, shall we?
This guide also includes information learned from the developers in forum conversations that was not, for whatever reason, included in the original combat guide.

Items not really covered in the combat guide

Q: What is "Critical Vulnerability" as seen in the captain's denounce and fire command talents?
A: Any future attacks against that target have their chance to critical increased by that percentage. I believe this is additive, so a soldier with 25% crit shooting a target with 10% critical vulnerability will have a 35% chance to crit.
Source: flat asked devs in a steam forum thread

Q: How does damage from fire tiles generated by Hydras work?
A: It's entirely based on the level of the talent that lit the square on fire. Passing through these squares deals a 10*talent level damage roll of fire damage, with the special damage 33% minimum rule applied. So a level 3 napalm charge will only deal 10-30 damage per tile passed through, while a level 9 would deal 30-90 per tile.
Source: Dev comments in the Neptune vs. Hydra community challenge (on a nonsteam forum)

Q: Wow, that's ruthless! I gave my hydra napalm charge 10 and lit a hall on fire. A skitterling ran through all of it, hit my hydra, and then exploded right before my turn.. what's up with that?
A: Indirect damage (Fire from tiles being the only one I know of) cannot reduce an enemy below 1 HP. At end of the round any enemy who is at 1 HP magically dies. It doesn't matter how they got down to 1.
Source: I think it's in combat basics but it might have come from the above nonsteam thread as well.

Q: So... burst fire looks like it targets 3 squares, but I'm having trouble hitting more than one enemy with it. Help?

A: Hoo boy, this one was an interesting steam thread. Nearly got it's own section. Basically there are two types of area attacks: cones and blasts.

Blasts include the hydra's ground placed fire abilities, all grenades, and Suppressing Fire from the neptune. Blasts also include all the melee attacks that hit multiple targets and the captain's crippling orders.
Blasts are easy to target, your target is the centerpoint and the spread is around it.
The hydra's blast attacks are unique among blasts in that they're tied to the tactics skill for number of targets directly hit by the attack.

Cones covers literally EVERYTHING ELSE that shows more than a singular target hit.
Cones you want to remember that the point of the cone is aimed at the shooter and it spreads away from the shooter.
Cones will miss EVERYTHING if they fail to hit the initial target of the attack.
Tips for cones: shoot the closer of the two (or more) enemies. don't be afraid to reposition a bit to have a weaker (easier to hit) enemy be the closer target.

Q: What about (obscura I forgot not covered here or in the combat guide)?
A: Comment. I'll get back to you. If you want a faster answer, the devs will probably respond within a day on steam forums. Then come comment here and let me know what they said so I can add it. :P

How does stealth work?

Honestly, I can't give you a whole lot past my observations and what I've read:

Facts first:
Stealth reduces the range at which enemies detect you while you have an active stealth buff (Overdrive, Null Field, that one ordinance I can't remember the name of and never use)
It does _not_ do this when you are not using one of those buffs.

Observations made during active stealth mode:
If an enemy is in range of your scout, that enemy will shoot (or maul) your scout barring a juicier target also in range. In that regard, scouts are a succulent watermelon to Xeno.
^ disproved by a local spitter in ironman that got within firing range but didnt kill my scout, saving the mission.

On brutal difficulty at reasonably high level, maxed stealth and overdrive 3 active meant I could get away with being a mere 2 spaces from a hunter and go unnoticed. (elevator stratos level, no other templars on that floor.)

Enemies can wander next to your scout while seeking other targets they can see. Then they're in range, then they're hitting you, then you're dead.

The elevator level of Stratos Orbital is a great scout training level for how to stealth. I did the top 2 floors with a total of 3 scouts. (one wasn't full stealth and only had overdrive 1. he got mauled by xeno and I had to send in a replacement. Second floor if you're wondering.)

Note that stealth can seem glitchy. I recently lost a scout on extermination protocol mission in ironman with 13 stealth +4 from null field +3 from overdrive when a pair of predators turned around and rushed him. I nearly lost another who got noticed by a skitterling 8 spaces away along with <level boss> and a hunter. (the second one didn't have null field though)
Thing is, the second one moved, crippling shotted enemies, and went back to dpsing his target. next turn they ignored him.
turn after they moved towards him again.
then away
then towards.
then my target died and I murdered them all.
He kept overdrive on the whole time, thus I honestly believe stealth is either:
1) not fully working as intended
-or-
2) intentionally unreliable.
The above is from an ironman game.

The parts of combat that can be ignored and the parts that cannot

This section is focused on defense, of both your templars and your enemies.
An attack has a few procedural steps it goes through that we learned in the combat basics guide:
1) is it auto blocked? (yes, that's the first thing they check. It doesn't change the math just let it go.)
2) does it hit (attack dice vs defense dice)
3) does it crit?
4) does it penetrate?
5) how much damage?
6) how much special damage?

Now let's look at each of these in depth:
1) Auto-block is amazing and I'm totally a fanboy of this statistic. That being said, in more general MMO terms it's "rogue tanking" where 1-2 attacks actually connect and you're splattified if this is your only defense. Capped at 59% + Focus (so 75% if stacking and high level)

2) I've fought my battles on this one because I'd rather not fight my battles WITH this one. Defense dice can only keep up (somewhat) with enemy attack dice if you're a shield using templar gearing specifically for that type of attack (melee or ranged). Even then, a goliath will laugh at your melee specialized defence and hit you anyways because his dice pool is rediculous. Hunters will hit you half the time and that's assuming you're using attacks to reduce their accuracy on top of doing everything you can to defend.
The best "defense" of the evasion statistic when I challenged that it was worthless on the forums was "not every class can get access to a decent amount of auto block".
Defense dice are spread over 2 types, 1 stat (Quickness), and 3 skills (Melee, Evasion, Tactics)
The hard cap for your Melee defense dice is 32 Strong and I think 21 Standard. Prior to reaching the character level required for this (Level 26 for captain) I'm fighting enemies that have 11S+77 attack. Three strong dice is approximately equal to 5 standard dice so they're swinging with 95 dice, I'm dodging with 75 (assuming I'm using the relic shield with 8 parry not the best nonrelic at 7 parry)

That same enemy has 8S+8 dice defending against getting shot. (they get a bit better dice in melee but not massively) meaning that gunnery and melee, strength and quickness _don't_ make a notable difference on if you hit!
^Ironman edit, these do matter a bit a top difficulties. Brutal on down I stand by my earlier statements.

This will be gone into more in the stats and skills section, basically: ignore defense dice, it's a cruel lie.

3) nothing you can do about this. someone should suggest an armor relic that reduces enemy critical chance, or perhaps an armor plating that does so. The more I think about it, I don't recall ever seeing an enemy crit.

4+5) does it penetrate.. AKA why do my berserks switch to paladin armor immediately. most enemies have around 20-40% penetration. specifically, the really weak (skitterlings) have maybe 20% the serious threat line troopers (hunters) have 40ish. There is a choice to be made here on what you want, be it armor value or deflection. Armors with high armor values tend to be easily pierced, armors with high deflection values tend to be lower armor values than their peers. I found this difference was most stark in the neptune armor options.
When I enter the late game I tend to go armor value > deflection because the enemy penetration is high enough that it's unlikely for deflection to occur. Armors with auto block or radiation resistsance get higher consideration regardless of this.

6) There's a tiny amount of fire damage in the game unless you're walking through your Hydra's AOEs. Radiation damage, OTOH, becomes very prevalent in the late game, albiet in smaller amounts. Rad resist is worthwhile late game. Fire resist is only worth it if your hydras are laying very hot fire where you'll later want to walk.

Stats and skills

This is where I diverge from standard thinking:
Stats first:

Fortitude: getting this to 8 should be an early priority for nearly every class. Scouts only need 4 because their defense is not getting attacked. Melee fighters should get to 10 after willpower is 4 but before focus training.

Willpower: most should seek 4 right after getting fortitude to 8. Engineers should seek 6 as this helps against overheat, and scouts should seek 8.

Focus: After reaching the above numbers, everyone should dump everything into here. Fort 8 will 4 is enough health to take a hit and a little bit of resistance to heat problems. Auto block is the best defense in the game _if_ you can take more than 2 hits, that's why the fortitude was first. Focus also boosts all critical damages, which you'll see later why a back line neptune wants the stat isn't about autoblock.

Strength and Quickness are junk stats. Don't waste your points here, you'll do better without them. Here's an updated version of what they do, taking into account the attack and defense dice disparity of enemies mentioned in the prior section:
Strength: Improves critical damage of melee attacks at the same rate as focus, without the auto block.
Quickness (ranged templar): Improves critical damage of ranged attacks at same rate as focus without the autoblock benefit.
Quickness (melee templar): improves counterattack chance by 1%, but since you always counterattack up to your limit per turn when blocking why not just block them with Focus?

Skills:
Melee (past 8) and Ranged are "I have nothing better to do with this point" skills. Evasion is "well, crap, melee is full now"

Exceptions should be made for templars who either 1) haven't ranked their attack talents very high, resulting in fewer bonus dice from talents or 2) Due to gear considerations are equipping weaponry with below average (for your team's level) accuracy bonuses. Those templars may want to get the relevant one of these to 6 first.

^ the above is for brutal difficulty and below.
I recently started a new game on Ironman (30th on leaderboards, woo hoo) and have been following this guide to the letter. I would change my advice, on such a high difficulty, to saying 1/3 of points should go into ranged for ranged combatants only, and 1/2 of points should go into melee for paladins. Berserkers should cap melee, as it's literally their only job. My captain is using a pistol and fire command, his stats are keeping melee 2 points below tactics and 2 points higher than ranged. This is the only edit I've made to advice offered thus far in the guide on that playthrough.

Tactics isn't really that great, all it does is allow your buffs to affect more people(if you even have buffs) and boost critical chance. Here's the thing: the other 3 stats shared by all templars are flat out worse. Max tactics first thing on anyone who is not 1) a scout, 2) an engineer, or 3) melee
Bonus: remember how we're stacking focus way high? That boosts critical damage :)

Special skills:
Grenades- this can be your post tactics dump if you're going to at least 5 in the talent. If not, this may need more points sooner. Do not stop at rank 1 grenade, only talent dice are strong on grenade accuracy rolls and with these your dicepool is weak enough that you can realistically miss. I wouldn't take this past 8 though. (note that +acc buffs and -dodge buffs can make grenades far more likely to hit. fire command 7 + 2 grenade 1 = pile of dead predators and commander still had 2 ap)

Stealth: priority #1, this boosts crit damage for sniper rifles meaning your scouts can rapidly get to the max of +192% damage on a critical. I'll try to do a section on how stealth works in brief to illustrate the other benefits. (this is a scout's defense stat!)

Engineering: This should always be your engineer's best stat. Splitting some into tactics early can still be a good thing though, especially if you use power field. After 6 tactics, I'd max engineer before finishing tactics. Since I don't use that talent, I just stack engineering.

Medic: I do _not_ max medic. I try to set my medic skill to work with my medic talent to heal about 60% of my paladin's health pool initially. I go for 80% later on. If you're waiting for someone to be below 40% before healing them, they'll probably die before you get around to it. If your medic can heal for more health than any member of your team actually _has_, you should downrank their medic skill or talent to put points elsewhere that they might serve you better.

Random tips and tricks (and mostly exploits)

Tips:
Hydras- targeting one of your "cover an area with fire" attacks on an enemy spawn point SHUTS OFF that spawn point. Note: you have to shoot the spawn point, not merely happen to bathe it in flames. Also, Hydras have the only debuffing attack that reduces enemy damage in the game. Get 2 (or more if you can spare them) points in redline reactor. For a boosted reactor using hydra, this can make the difference between shutting down near the enemy and shutting down.. well, nowhere near the enemy.

Paladins and Berserkers- If you're ignoring my "defense dice are useless" rhetoric, -ACC talents take away strong dice first, then remove standard dice with any left over. These could be the key to making misses happen. :) (changelog 7/7/17)
Paladins and Berserkers, again-Passive capping your Autoblock is nice but make sure your weapon is still worth a care. Don't go below a 5 point weapon or your counterattacks will make you regret your life decisions.

Neptunes- Get Deadly Burst 1. It's the only neptune attack that allows you to move after firing, and is worthwhile for that factor alone. Suppressing fire 5 and Full Auto 5 are nice, I only go to Manual Vent 2.

Scouts- overdrive 3 is the point where it stops granting 1 MP per talent rank. Crippling shot 3 is -3MP, which will near immobilize anything but skitterlings. MP cannot be reduced below 1 (I've tried)

Engineers- take a good look at capture rank 6 compared to capture rank 5. That's the rank where it goes down to taking 2 AP to use, meaning you can do it twice per turn, meaning max time to capture a point with that engineer is 2 turns.

Soldiers can get the highest static critical chance in the game using NX-Jacket rounds plus Vital Core Lock trinkets, at 27% from gear with another 16% from maxed tactics for 43% basic. Also getting the most HP per fortitude point and the second best buffs in the game (hats off to Paladins) don't underestimate these guys. There's a reason vanilla ice cream is the most popular flavor by a massive margin. (Personally I favor chocolate neptune, but that's just me)

Tricks (this is stuff that just works for me and doesn't violate the spirit of the game):
Roar's Talon + StrikePoint Kit relic pairing. This gets rediculous so fast it ain't even funny. Add Shredding Fire rank 10 and hilarity ensues.


Exploits (AKA this here be the cheatin' way, but I teach methods not morality):
How to violate gear allocation to equip way better weapons early-midgame:
I did this by accident with my neptunes in my first game but it could easily be done with any class.
Basically, go deep and unlock some top tier non relic weapon in the requisition tree.
Fire ever templar you have of that class (except Dalan Ortho because we love Dalan Ortho)
Go into an open deployment mission
Do everything in your power to bring in as many new recruits of that class as you can
They will come with basic attack ranked as high as their level allows and the best weapon _unlocked_ for their class. Note that if you remove the weapon, you won't be able to put it back on until far later when you actually have the gear allocation to use it. Note that they're not restricted to what you've unlocked for that primary attack's skill rank either.

How to get the sentry turret skill without going into the engineer tree:
Hire a new engineer with none left in your veteran roster, or better yet, fire the old one before starting a level requiring one. Engineers are an exception to the "maxed primary attack skill" rule used above, their "primary attack" is apparently considered to be sentry turrets. I can't disagree with the devs on that one.

There was once a flat out cheat listed. Then I had duplication issues with it. Then I realized the paladin who initially did it had "counterattacks cost nothing" from cascading tact relic. Working as intended lol, my bad :P

[Fushiii]

This is great! Thanks

[Terminarch]

I'm super late here, but do you have any input on when enemies are allowed to spawn from a spawn point? You mention Hydra flames but I'd like more detailed information on preventing 'it spawned and attacked same turn from max move range' nastiness.

[Loyal Viggo]

Thanks OP.

[FlavorTown]

indepth but understandable, very useful stuff here.

[mal]

7/17/17 update: included some unreliability notes on stealth, mitigated my "to hit doesn't matter" stance for top difficulties because on ironman I'm feeling it, edited out the flat cheat that was caused by me not realizing _which_ paladin I was using (his relic explained it) and added note that I don't think enemies _can_ crit, because I haven't observed it in a lot of combat log diving.
Also corrected my statement on combat dice, 3 strong = 5 standard within the systems math. (according to dev statements in forums)