The gravitational field of massive objects in the universe bends the path of approaching light rays, and leads to an apparent distortion in the shapes of background galaxies. The statistical measurement of this effect, known as Weak Lensing (WL), has become a fundamental tool for observational cosmology, on par with studies of the Cosmic Microwave Background and Supernovae. The strength of this method is that it probes the total intervening mass distribution, including the Dark Matter mass component. Furthermore, by tracking the growth of this mass distribution as the universe expands, WL also provides a measure of Dark Energy. Finally, WL can also be used as a powerful tool to elucidate the connection between galaxy formation processes and the underlying Dark Matter distribution. The scientific promise of WL has inspired the development of a large number of surveys that will image large swaths of the sky in the next two decades (HSC, DES, EUCLID, etc ..). In this talk, I will present a broad overview of how WL will be used in these surveys to simultaneously tackle outstanding questions related to Dark Energy, Dark Matter, and to advance our understanding of galaxy formation.