Abstract: Infinite projected entangled pair states (iPEPS) can be used to classically simulate 2D strongly correlated systems of infinite size. Here we present a number of recent developments. In particular, we explain how the use of corner transfer matrices for tensor network contraction can enhance the efficiency and accuracy of the iPEPS method when compared to using 1D transfer matrix techniques, and how (in the context of fermionic tensor networks) it can be adapted to simulate fermionic quantum lattice systems.