A fundamental goal in observational cosmology is to understand the link between the luminous properties of galaxies and the dark matter halos in which they reside. A precise understanding of the key mechanisms that determine the growth, evolution, and global properties of galaxies has eluded astronomers for more than half a century. Dark matter is thought to play a key role in setting the conditions that determine galaxy properties but the exact details of how dark matter influences galaxy formation remains a topic of active debate. Weak lensing, which relies simply on the laws of gravity, is a unique method that can be used to directly probe the dark matter components of galaxies. While previous weak lensing surveys have been modest, reaching at most a few hundred square degrees, the state-of-the art in this field is changing dramatically with surveys such as the Hyper Suprime Cam (HSC) survey, an ambitious multi-wavelength (g,r,i,z,y) weak-lensing program to map out 1500 square degrees of the sky with the 8.2m Subaru Telescope to i∼26 mag. Euclid, WFIRST and LSST will follow in less than a decade. In this talk, I will discuss new frontiers that are opening up with these expanded data-sets. New programs that will soon be within reach include detailed studies of the interconnected assembly histories of massive galaxies and dark matter, lensing-based constraints on the inner profiles of dark matter halos and possibly also of the stellar Initial Mass Function (IMF), and direct measurements of the halo masses of dwarf galaxies.