We present a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar N=4 SYM theory. It takes the form of a Y-system based on the integrability of the dual superstring sigma-model on the AdS5 x S5 background. This Y-system passes some very important tests: it reproduces the full asymptotic Bethe ansatz at large L, including the dressing factor, and it confirms all recently found wrapping corrections. We shall also describe the derivation of these equations in some detail.