This guide will cover all the ways you can upgrade and develop your Titans.
LEVELING UP
Just like Invokers, you can level up Titans using XP Potions. Leveling them up increases their Stats.
Note: Unlike Invokers, Titans do not gain XP from battles. You must use XP Potions.

You cannot Level Up Titans indefinitely – there is a limit, a Level Cap decided by the Titan's current Ascension ★.
Once you hit that Level Cap, you must Ascend your Invoker to continue Levelling them up and making them stronger. The highest Level a Titan can reach is Level 60.

ASCENSION

In a Titan's profile, a series of yellow Stars that show the Titan's Ascension level.
In the screenshot above, Goros is at 3★ Ascension.
Ascending Titans increases their Level Cap, and allows you to continue to Level them up and make them stronger. Each Titan can be Ascended up to 6★ Ascension, which sets the Level Cap to Level 60 – the highest possible Level.

To Ascend a Titan, they must be at the Level Cap for their current Level of Ascension.
To Ascend them, you will need to use a number of Dragonsouls or other Titans of the same ★.
The number you need is always equal to the current Ascension ★.
For example, to take a Titan from 3★ Ascension to 4★ Ascension, you need three 3★ Titans or 3★ Dragonsouls – or a mixture of both. This is shown in the screenshot above.
To take a Titan from 4★ Ascension to 5★, you will need 4 Titans or Dragonsouls – all 4★.
Note: Any Titans used to Ascend another will be permanently lost.

After Ascending a Titan, they will gain an extra yellow star and their Level Cap will increase.

Different Rarities of Titans start at various levels of Ascension, as shown below:
EMPOWERMENT

Purple Stars show a Titan's Empowerment Level.
In the example above, Goros is at:
1★ Empowerment (indicated by the purple star)
4★ Ascension (indicated by the yellow stars)

Empowering a Titan improves their Bound Effect, which increases the Stat boost they provide to your Invokers during battle.
To Empower a Titan, you need to use Titanhearts or duplicates of the same Titan.
There are 2 types of Titanhearts:
Titanhearts
Elder Titanhearts
Both types of Titanhearts can be found by completing Quests, at the Shop, or as reward from various Game Modes.

Depending on a Titan's Rarity, you will need different types or a different number of Titanhearts.
Rare Titans: 1 Titanheart or 1 duplicate Titan
Epic Titans: 2 Titanhearts or 1 duplicate Titan
Legendary Titans: 1 Elder Titanheart or 1 duplicate Titan
Empowerment requirements do not change at higher Empowerment ★.
Note: Any Titans used to Empower another will be permanently lost.

After Empowering a Titan, their Bound Effect will improve.