Kicks are an integral part of tricking, and arguably 1/3rd of tricking techniques. The history of tricking lies in martial arts, but there is much more to it now. We still base a lot of what we learn on the martial arts aspects, even using the kicks to learn how to do the twists and flips.
There are many variations of kicks, especially when you count all the twists and flips you can combine with kicks, but they generally boil down to just 4 different kicks and variations. Here are some links to a Youtuber called Kwonkicker and his tutorials for the 4 basic kicks. It's important to note - MANY trickers end up using Crescent kicks in lieu of a proper Round or Hook kick, as the Crescent is infinitely easier... HOWEVER... some tricks are meant to be Crescent kicks.
Hook and Spinning Hook Kick
Inside Crescent kick is frequently used before mastery of the Round kick in tricking...
...and the Outside Crescent is frequently used before the Hook kick is mastered.