Due to their low halo mass, dwarf galaxies have long been thought to be more sensitive to their environment and to the details of star formation feedback than are more massive galaxies. However, the intrinsic faintness of these low-mass systems have historically precluded the execution of detailed studies of dwarfs outside the nearby Universe. Now, current generation imaging surveys are opening a new avenue for studies of dwarfs and their structure in large samples out to intermediate redshifts. I will discuss results in the realm of dwarf structure and star formation from the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) imaging survey, as well as a comparison between the structure of observed dwarfs and the simulated galaxies of the FIRE-2 simulation suite. I will discuss both “normal” dwarfs and their “extreme” ultra-diffuse counterparts, and gesture forwards towards the advent of a low-mass galaxy census made possible by next generation surveys.