Ray chaos, characterized by eventual exponential divergence of originally nearby multi-bounce ray trajectories, is an intriguing phenomenon. It can be observed in several electromagnetic wave propagation scenarios: both very complex (e.g., urban areas) and very simple (e.g., a stadium-shaped cavity) scenarios. This paper contains a compact review of known results on wave propagation in ray-chaotic scenarios. Attention is focused principally on two-dimensional simple paradigms of internal ray chaos (“ray-chaotic billiards”), with emphasis on possible implications for high-frequency wave dynamics (“ray-chaotic footprints”). General concepts, tools, and numerical examples are discussed, and their potential relevance to current challenges in electromagnetic engineering is noted.