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Billiards are a class of dynamical systems in which a point particle moves uniformly in a domain $D\subset \mathbb{R}^d$ except for mirror-like reflections from the boundary. Varying $D$ leads to examples satisfying many ergodic properties. Billiards enhance visual explanations of dynamical concepts to students and the general public. There are many applications in physics and image processing. The free motion and/or reflection rule may be generalized.

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What "real life" problems can be solved using billiards?

The keyword you are looking for is " Microorganism Billiards". Very recent topic, but now seems to be catching up in fluids/bio community. …
Piyush Grover's user avatar