Photon-enhanced thermionic emission (PETE) converts sunlight to electricity with the combined photonic and thermal excitation of charge carriers in a semiconductor, leading to electron emission over a vacuum gap. Theoretical analyses predict conversion efficiency that can match, or even exceed, the efficiency of traditional solar thermal and photovoltaic converters. Several materials have been examined as candidates for radiation absorbers and electron emitters, with no conclusion yet on the best set of materials to achieve high efficiency. Analyses have shown the complexity of the energy conversion and transport processes, and the significance of several loss mechanisms, requiring careful control of material properties and optimization of the device structure. Here we survey current research on PETE modeling, materials, and device configurations, outline the advances made, and stress the open issues and future research needed. Based on the substantial progress already made in this young topic, and the potential of high conversion efficiency based on theoretical performance limits, continued research in this direction is very promising and may yield a competitive technology for solar electricity generation.