DOTTORATO DI RICERCA IN FISICA, ASTROFISICA E FISICA APPLICATA PHYSICS COLLOQUIUM ABSTRACT: In appropriate limits, gravitational fields can be assigned an index of refraction, which allows gravitational lensing effects to be described like ordinary geometrical optics. Despite its conceptual simplicity, gravitational lensing is perhaps one of the most promising methods to study structures of dark matter in a universe dominated by dark energy. I shall describe the foundations of gravitational lensing and discuss some of its applications on all scales in astrophysics: microlensing, lensing by galaxies and galaxy clusters, and the weak coherent lensing effects of large-scale cosmic structures.