Weak gravitational lensing of faint background galaxies has now been detected and used to measure the amplitude of dark matter fluctuations in the Universe. Recent theoretical work has demonstrated that there is a vast amount of information on the matter and energy content of the Universe available from the weak lensing signal. Space-based weak lensing surveys should be able to reconstruct the history of the dark energy equation of state, determine the masses of the neutrinos, and test the predictions of inflation, all to much higher accuracy than is possible with CMB measurements alone. I briefly describe these methods and the expected progress toward their exploitation from space- and ground-based experiments.