Computer-Based Animation
Above is the a clip fro the show 'RWBY' by RoosterTeeth.
The animation style is animated on a computer, so there is some things that are easier and an example of computer-based animation. The animation software they use is actually something that takes a lot of time (mainly via key-framing), but they use the framing system to create the vision of movement.
Some of the fight scenes have some impressive stuff as they have 'Motion-Capture' with suits so they can do some fast-paced moments.
Below is another example of computer-based animation, 'Red vs Blue' by RoosterTeeth, also using similar techniques and moments in the show, based off of another series.
Traditional Animation
Above is a clip from the series 'Soul Eater' written by Atsushi Ōkubo, in which one of the partners has to face off against another combination of a weapon and a meister. This kind of animation is based off of drawings placed together in a sequence, you draw one drawing, then another one after it with a slight adjustment and soon they are placed together and then the animation comes to life.
It comes off very interesting as a result but is the most time consuming. At about 12-25 drawings a second, there are some moments slicker than others but it's eye-candy to those observing.
Another example of traditional animation which is also of a Japanese descent is Death Note, using very similar if not the same kinds of techniques.
Stop-Motion Animation
Above is a clip from 'Wallace & Gromit: The Wrong Trousers' by Aardman, in which Wallace & Gromit chase after the Penguin thief 'Feathers McGraw'.
This kind of animation is one of, if not the most time-consuming, it involves making and sculpting clay models and then placing them in a position. After that you take a picture, like a photograph, then you move them ever so slightly, and take another picture, after that you move on to the next frame, and the next frame and so forth. Another example of this kind of animation is placed below, known as Morph, also by Aardman.