When the QED vacuum is probed with extremely intense electromagnetic fields, several novel vacuum polarization effects are expected to occur, but which have not yet been directly observed. The best known is the Heisenberg-Schwinger effect, the "boiling of the vacuum," in which electron-positron pairs are created from vacuum. Others include peculiar features of nonlinear Compton scattering, and the fundamental problem of understanding radiation reaction. There is also strong motivation from particle physics and gravity to understand these processes more precisely. The prospect of precision experiments with ultra-intense lasers, and combining these with high energy electron beams, brings together aspects of laser physics, plasma physics, and particle physics, and suggests that it may soon be possible to probe some of these nonlinear QED effects with precision. I will give a general overview of the field.