Nonlinear effects in photoemission are shown to open an access to the band structure of unoccupied states in solids, totally different from hitherto used photoemission spectroscopy. Despite its second-order nature, strong resonant transitions occur, obeying exact selection rules of energy, crystal symmetry, and momentum. Ab initio calculations are performed to demonstrate that such structures are present in low-energy laser spectroscopy experimental measurements on Si. Similar resonances are predicted in ultraviolet angle-resolved photoemission spectra, as shown with a theoretical calculation on bulk Al.