The evidence from NMR experiments for the existence of strong temperature dependent antiferromagnetic correlations among nearly localized Cu2+ spins in the cuprate oxide planes is reviewed. It leads naturally to a description of the normal state as a nearly antiferromagnetic Fermi liquid in which the magnetic excitations are commensurate, or very nearly so, antiferromagnetic paramagnons whose spectrum at low frequencies can be obtained from fits to NMR experiments, and whose coupling to quasiparticles on a 2D square lattice is responsible for the measured anomalous transport and optical properties. Recent work by Monthoux, Balatsky and Pines demonstrates that the retarded quasiparticle interaction induced by these paramagnons can lead to a superconducting state with dx2-y2 symmetry, a high transition temperature, and energy gap behavior comparable to those measured. NMR experiments on the superconducting state are shown to support d-wave pairing, while existing penetration depth experiments do not appear to provide conclusive evidence concerning the pairing state.