Pulsar emission should come primarily from the magnetic separatrix. Combining theory and observations, we show that force-free electrodynamics (FFE) gives an accurate description of the large-scale electromagnetic field in the magnetospheres of Crab-like pulsars. A robust prediction of FFE is the existence and stability of a singular current layer on the magnetic separatrix. We argue that most of the observed pulsar emission comes from this singular current layer.