We argue that many features of the structure of nuclei can be understood in the unitarity limit, where the two-nucleon S-waves have bound states at zero energy. In this limit, the only dimensionful parameter, related to the breaking of scale invariance to a discrete scaling symmetry, is set by the triton binding energy. For A <= 4 nucleons, we demonstrate that the spectrum can be obtained as a controlled perturbative expansion around the unitarity limit.