The bulk photovoltaic effect refers to the generation of photocurrents and photovoltages in bulk single-phase materials. It requires only that the material possess broken inversion symmetry, and occurs due a unique mechanism known as "shift current." Discovered over a half-century ago, it received little attention decades due to extremely poor observed efficiency. However, in recent years, it has been both theoretically and experimentally investigated in a variety of new systems and materials, and significant improvements in performance have been achieved. In this talk, I will provide a brief overview of the physics of the bulk photovoltaic effect and survey the experimental and theoretical advances that have been made in its understanding and optimization. I will cover in detail the unique properties of the bulk photovoltaic effect that distinguish it from conventional photovoltaic effects, including photovoltages substantially exceeding the material's band gap, response amplitudes and directions that can depend on both photon energy and polarization, and response that occurs on ultrafast timescales. Finally, I will explore the potential for these features to enable novel and improved photosensitive devices, especially in combination with other functional materials.