Weyl semimetals are topological materials whose electron quasiparticles obey the Weyl equation. They possess many unusual properties that may lead to new applications. This is a tutorial review of the optical properties and applications of Weyl semimetals. We review the basic concepts and optical responses of Weyl semimetals, and survey their applications in optics and thermal photonics. We hope this pedagogical text will motivate further research on this emerging topic.