This article describes advances in thermionic and photo-emission materials and applications dating back to the work on thermionic emission by Guthrie (1873) and the photoelectric effect by Hertz (1893). Thermionic emission has been employed for electron beam generation from Edison's work with the light bulb to modern day technologies such as scanning and transmission electron microscopy. The photoelectric effect has been utilized in common devices such as cameras and photocopiers while photovoltaic cells continue to be widely successful and further researched. Limitations in device efficiency and materials have thus far restricted large-scale energy generation sources based on thermionic and photoemission. However, recent advances in the fabrication of nanoscale emitters suggest promising routes for improving both thermionic and photo-enhanced electron emission along with newly developed research concepts, e.g., photonically enhanced thermionic emission. However, the abundance of new emitter materials and reduced dimensions of some nanoscale emitters increases the complexity of electron-emission theory and engender new questions related to the dimensionality of the emitter. This work presents derivations of basic two and three-dimensional thermionic and photo-emission theory along with comparisons to experimentally acquired data. The resulting theory can be applied to many different material types regardless of composition, bulk, and surface structure.