Weak gravitational lensing is a unique probe of the dark side of the universe: It provides a direct way to map the distribution of dark matter around galaxies and clusters of galaxies as well as on cosmological scales. Furthermore, the measurement of the weak lensing–induced distortions of the shapes of distant galaxies is a potentially powerful probe of dark energy. In this review we discuss how this challenging measurement is made and interpreted. We describe the various systematic effects that can hamper progress and how they may be overcome. We review some of the recent results in weak lensing by galaxies, galaxy clusters, and cosmic shear and discuss the prospects for dark energy measurements from planned surveys.