Bright electron beams, as well as the technologies they power, are among the most powerful probes of matter at atomic length and time scales. Many of these systems and techniques, however, are limited in performance by the achievable brightness of modern particle accelerators. This thesis first investigates the factors that limit the final brightness of electron beams. These results suggest that research into better photocathode technologies is a viable path toward improving brightness in contemporary accelerator systems. The remainder of this thesis is dedicated to exploring a diverse set of ideas on how to improve the quality of photocathodes. First, brightness from Cs-Te (a common semiconductor photocathode) is measured near the photoemission threshold. Tuning the photon energy of the driving laser close to the threshold is expected to limit the energy imparted to the emitted electrons and improve the beam's initial brightness. Instead, it is revealed that low workfunction impurities likely present in cathodes of this type may be a barrier to high brightness. Next, we investigate a novel method of emitting electrons from unoccupied states with low transverse momentum. Electrons are first excited within a semiconductor and then ejected in a pump-prove style experiment. By adding a delay between the two processes, the electrons may relax and lose energy which may result in better brightness. Finally, the fabrication of nanoscale patterns on the surface of metal cathodes is investigated as a way to improve their nonlinear yield and source size. Future directions in research on the brightness of electron sources are discussed.