We give the first rigorous formulation and proof of an area theorem for cosmology. Holographic screens track the fundamental information content of arbitrary spacetimes. By construction, a holographic screen hypersurface $H$ admits a foliation into marginal surfaces (``leaves''), which have vanishing null expansion in one direction. The sign of the other null expansion allows us to distinguish between marginally trapped and antitrapped leaves. This gives rise to the more refined notions of futur holographic screens, which exist inside black holes; and past holographic screens, which exist in an expanding universe. With this refinement, the area of leaves grows monotonically if the null curvature condition holds. The proof is nontrivial and exploits nonlocal properties of the light-sheets emanating from the screen. The quantum extension of our result becomes a precise statement of a generalized second law, with a standard arrow of time in cosmology but, remarkably, an inverted arrow of time in collapsing regions.