Near- and sub-wavelength photonic structures are used by numerous organisms (e.g. insects, cephalopods, fish, birds) to create vivid and often dynamically-tunable colors, as well as create, manipulate, or capture light for vision, communication, crypsis, photosynthesis, and defense. This review introduces the physics of moth eye (ME)-like, biomimetic nanostructures and discusses their application to reduce optical losses and improve efficiency of various optoelectronic devices, including photodetectors, photovoltaics, imagers, and light emitting diodes. Light-matter interactions at structured and heterogeneous surfaces over different length scales are discussed, as are the various methods used to create ME-inspired surfaces. Special interest is placed on a simple, scalable, and tunable method, namely colloidal lithography with plasma dry etching, to fabricate ME-inspired nanostructures in a vast suite of materials. Anti-reflective surfaces and coatings for IR devices and enhancing light extraction from visible light emitting diodes are highlighted.