Reducing the reflection and improving the transmission or absorption of light from wide angles of incidence in a broad wavelength range are crucial for enhancing the performance of the optical, optoelectronic, and electro-optical devices. Inspired by the structures of the insect compound eyes, nanostructure arrays (NSAs) have been developed as effective antireflective surfaces, which exhibit promising broadband and quasi-omnidirectional antireflective properties together with multifunctions. This review summarizes the recent advances in the fabrication and performance of antireflective surfaces based on NSAs of a wide variety of materials including silicon and non-silicon materials. The applications of the NSA-based antireflective surfaces in solar cells, light emitting diodes, detection, and imaging are highlighted. The remaining challenges along with future trends in NSA-based antireflective surfaces are also discussed.