In the first part of the present review paper, experimental results which lead to the discovery of two-proton radioactivity are reviewed. Beyond two-proton emission from nuclear ground states, we also discuss experimental studies of two-proton emission from excited states populated either by nuclear beta decay or by inelastic reactions. In the second part, we review the modern theory of two-proton radioactivity. An outlook to future experimental studies and theoretical developments will conclude this review.