You can grow your Fiends with Meteormites.
Each upgrade requires a different amount of yellow and/or blue Meteormites. Every time you upgrade your Fiend, it increases his/her attack power.
In addition to attack power; every fifth upgrade *up to level 20* also improves the special power of your Fiends.
You will start finding yellow Meteormites very early in the game. Blue Meteormites appear a little later in the game.
They are more rare and more valuable than yellow Meteormites. To grow a Fiend, navigate to the Fiendex (the button in the bottom-right corner of the world map screen), then to the Fiend you wish to upgrade. Tap on the Fiend of your choice to view their information, as well as how much it costs to grow them.
To upgrade the Fiend, simply tap the Upgrade button. If your Fiend is about to reach their 5th, 10th, 15, or 20th level, this button will read Evolve to signify that they will be evolving into a more powerful form - their special power will also improve.
If you do not have enough Meteormites to complete an upgrade then you can use another resource to compensate for the missing Meteormites.
You can find free Meteormites by opening cages with keys at the end of each level or by competing in the various in-game events!