We study the emission of two protons from nuclei where this is the only decay channel. A three-body model is developed. We compare the "diproton" model with the three-body calculations. We present exploratory studies of the 19Mg and 48Ni ground states, which are good candidates for two-proton radioactivity. The two-proton width for the 17Ne 3/2(-) state is also estimated. Our calculations give substantially lower values for the width than predicted by the diproton model, but larger than from direct decay to the continuum.