Abstract: Tiling billiards is a new dynamical system where a beam of light refracts through a planar tiling. It turns out that, for a regular tiling of the plane by congruent triangles, the light trajectories can be described by interval exchange transformations. I will explain this surprising correspondence, give some results, and show computer simulations of the system. This system was first studied at Summer@ICERM in 2012 and 2013.