Low-surface-brightness (LSB) galaxies, a heterogeneous population ranging from dwarfs to large, diffuse spirals, are faint systems that are largely invisible in past surveys (e.g. the SDSS). However, LSB galaxies dominate the local number density and understanding their formation is central to a complete understanding of galaxy evolution. Using a cosmological hydro-dynamical simulation, we explore how these systems form and why they diverge so strongly from their high-surface-brightness counterparts over cosmic time. We show that, at high redshift (z~3), LSB progenitors have stronger, burstier star formation. The resultant stronger stellar feedback flattens their gas-density profiles, by displacing cold gas (but does not quench star formation). These flatter gas profiles, in turn, produce flatter stellar systems, which are more susceptible to tidal processes. Over time, heating and stripping due to the ambient tidal field drive rapid (cold) gas loss and a strong increase in effective radii, that produces today’s LSB systems. In clusters, ram-pressure stripping provides an additional mechanism that assists in this evolution (although tidal heating/stripping remains the principal mechanism of LSB galaxy formation even in these ultra-dense environments). The LSB Universe is a new frontier in the study of galaxy evolution and offers a vast, untapped discovery space that is perfectly aligned with the capabilities of new surveys like the Hyper Suprime Cam survey and, in the near future, LSST.