By definition, anime is all about the animation. Even still, the styles and elements of animation can vary massively from anime to anime, and especially from animator to animator. Different artists have different styles, paying attention to individual details and emphasizing some things over others.
I'll be honest, I'm not super well versed in the field of anime animators and animation studios, not as well as I should be. But there is one animator that I know I've enjoyed a lot, and I only found out about him because he's worked on two separate anime I've watched in the last year or two.
He is Key Animator Arifumi Imai.
He was (is?) the lead animator on Attack on Titan, though that wasn't his first work in that capacity. He is responsible for the fast-paced and intense animation of the anime, scenes like this one with Levi above.
AOT, which can be a kind of dark anime visually, is still vibrantly colorful, something that is a staple of Arifumi's work. Even in this scene, in a dark and wooded area, there is color in the bright light of Levi's swords and the sunlight behind him as he blinds the female titan.
Arifumi is using the brightness of the blades and the angle of the camera to show action and speed. The color plays into that - the blood on her arm, the sparks that fly off of his impact show just how much force is in these movements.
Arifumi was also a key animator for One Punch Man, another anime with incredible, tight action sequences and vibrant color. OPM is without a doubt more colorful than AOT, and certainly one of the most colorful anime I've seen overall.
In his animation, Arifumi plays color as an agent of the action. Color makes things vivid and bright, and more explosive and eye catching. In OPM some of it is intentionally overblown, since that's the nature of the whole anime, but even in his other work, Arifumi uses bright color to make very detailed and action-driven sequences.
The brilliant contrasts highlight all the best parts of the sequences, shining literal lights on them. It makes the action engaging as well as easy to keep up with.
I couldn't find appropriate gifs for the awesomeness of the animation, so just watch this awesome amv that showcases the brightness and intensity of Saitama's fight with Boros.
And a great big thank you to Arifumi Imai, for making the art he does.