Certain many-body quantum systems can be efficiently described in terms of Projected Entangled-Pair States (PEPS). In this talk I will review some of the properties of such states, paying special attention to the bulk-boundary correspondence they define. In particular, I will show how topological properties are reflected in the theory of the boundary. This work was done in collaboration with D. Pérez García, D. Poilblanc, N. Schuch and F. Verstraete.