This guide will cover exactly how Titans work during battle, covering Invokation, Stats, and a Titan's effect on the Invoker they're bound to.

TITAN MANA
Your team will generate Titan Mana alongside Ultimate Mana when they use their Combo Attacks and Skills during combat.
Using Skills outside of combat (like after you clear all the enemies in the area) will not generate either Ultimate Mana or Titan Mana.
Important! Even though each Invoker generates Titan Mana individually, it goes into a pool that is shared by the whole team. When a Titan is Invoked, Titan Mana is spent from the whole team's supply.
This is different to Ultimate Mana, where each Invoker has their own, individual pool.
TITAN MANA METER

Your Titan Meter is displayed at the bottom of your screen during battle.

When your team has enough Titan Mana, it's Invokation Time: Titan Cards will appear at the bottom of your screen.
Hit the Card and that Invoker will Invoke their Titan – even if you're not controlling them at the time.
Meter Overflow. It's not always the right time to Invoke a Titan – if it's four Invokers against a single straggling Goblin, you might want to hold your Titans for later. Don't worry, your Titan Mana Meter has an overflow; you'll still be able to generate and store Titan Mana without wasting it.
Pro Tip: Increasing Mana Gen affects both Ultimate and Titan Mana. Higher Mana Gen means you'll be able to Invoke Titans more frequently in-battle, which is one of the best ways to increase your team's damage output.
INVOKATION LIMIT
You can only Invoke one Titan at a time during battle.
INVOKATION DURATION

By default, whenever a Titan is Invoked during battle, Titan Invokation Time lasts 12 seconds.
After 12 seconds, Invokation will end and the Titan will transform back into the Invoker.
Each Titan has their own cooldown – 180 seconds – before they can be Invoked again. This cooldown starts after the Invokation ends, not when it starts.
Make sure each Invoker in your team has a Titan bound to them to maximize your Titans’ impact in battle.

Pro Tip #1. You can increase Titan Invokation Time by Awakening your Invokers. At 2★, 4★, and 6★ Awakening, each Invoker will have an Invokation Node. Each one will increase the duration of Invokation Time by 1s. It doesn't sound like much, but increasing Invokation time from 12 to 15 seconds means a huge, huge increase in damage output for a Titan.
Pro Tip #2. An Invoker's Skill Cooldowns will continue to count down as normal even while they are currently in Titan form.
Pro Tip #3. Any Buffs and Debuffs on the Invoker (or Titan) at the time of Invokation or Invokation End will carry through and continue. Invoking a Titan isn't a quick way to cleanse pesky debuffs.
Pro Tip #4. Titans don't generate any Ultimate Mana for their Invoker or Titan Mana for their team.
INVOKATION EFFECTS

Each Titan has a unique Invokation Effect, which has two parts:
Invokation: Whenever a Titan is Invoked in-battle, a powerful Invokation effect occurs. This is usually a huge AoE ability that affects all the enemies or allies around them.
Invokation End: When the Invokation ends and the Titan transforms back into their Invoker, a second powerful effect occurs. This is typically a big buff or heal to the Invoker the Titan is bound to, giving them a massive boost when they come back into the fight.
You can upgrade Invokation Effects just like regular Titan Skills, with Prisms and Gold.
TITAN STATS
INVOKED TITAN STATS

When you use a Titan in-battle, its Stats are based on the Invoker they are bound to. The better the Invoker's Stats, the better the Titan's.
Titans have three types of Stats:
Percentage Stats: These percentages are added to the Invoker's Base Stats (excluding any Stat boosts the Invoker has from Relics or other sources). As the Titan levels up, these Stats increase.
Flat Stats: These are integer stats (raw numbers) that are added on top, after all other Stats have been calculated. As the Titan levels up, these Stats increase.
Titan Class Bonus Stat. There are two Classes of Titan: Tank and Attack. Depending on the Class, the Titan will either have a DEF% or Crit Rate% Bonus Stat. The number depends on the Rarity of the Titan and does not increase as the Titan levels up.
NOTE: This is the current system and will soon be changed, along with an improved UI to clarify the functionality. We are removing the static Titan Class Bonus Stat – it will function like all other stats and increase as the Titan levels up.
TITAN CLASS STATS
There are two Classes of Titan: Tank and Attack, each with different percentage-based Stats.
Tank Titans have: Invoker HP%, DEF%, and ATK%
Attack Titans have: Invoker Crit Rate%, Crit DMG%, and ATK%.
Both Classes have HP, DEF, and ATK as flat Stats.
BOUND EFFECT

Titans also increase the Stats of the Invoker they are bound to during battle. This is called their Bound Effect.
There are two types of Bound Effects:
Type 1: Global Bound Effects that increase an Invoker's Stats in every area of the game.
Type 2: Dual Bound Effects that increase an Invoker's Stats by a larger amount in a specific area, along with a lesser amount in other areas of the game. These are usually more powerful in a specific Game Mode, but weaker outside of that designated Game Mode.

In the picture above, Goros has a Dual Bound Effect.