Among the many phenomena of the light-matter interaction in complex materials the conversion of incident light into a dc-current seems particularly tantalizing. However, in semiconductors this bulk photovoltaic effect is normally small. Recently, experiments in Weyl semimetals have revealed an unusually large second-order optical response. This has called into question the established explanation by a dynamical shift of the center of mass in a wavepacket. I discuss the second-order dc current in realistic systems with finite quasiparticle lifetimes, focusing on the consequences of the time-reversal-symmetry breaking. Three mechanisms which generate a dc-photocurrent emerge, i.e. the Berry curvature, the quantum metric and the diabatic motion. All three effects can be understood semiclassically from the anomalous acceleration of the quasiparticles.