What are Bézier curves, and why should I care?

Bézier curves are used for a lot of things in computer graphics: smooth transitions, scalable shapes, and can be used to outline movement in animation. However, they're used in the real world as well, in things like railway route or highway modeling, robotics, and more. In fact, the Bézier curve is named after a French engineer, Pierre Bézier, who used it in the 1960s for designing curves for the bodywork of Renault cars.

They're also quite cool, when you really get to understand how they work.