Pixar gets its characters to move and emote by building them rigs and filling them with controls that allow animators to give them unique expressions and movements. "Toy Story 2" gave them the ability to adapt and reuse rigs for multiple characters, allowing a wide array of characters of all shapes and sizes.
In "Finding Nemo," animators learned how to make fish show emotions despite their lack of eyebrows. Major breakthroughs occurred during "The Incredibles," in which animators now had the capability to give humans muscles and skin that moved like the real thing, eventually allowing "Ratatouille" to stretch the human mouth far and control a character's loose movements.
Meanwhile in "Cars," a new technology called ground locking let cars drive on a straight path, while new stretchy rigs were created for realistic octopus tentacles in "Finding Dory" and an especially dynamic dog tongue in "Coco."
Thanks to new features, like the ability to add tendons onto hands and a digital piano that played by itself, Pixar was able to show complex piano playing.
None of it would have been possible without the animation and rigging breakthroughs that came before it.