The ab initio multiple spawning (AIMS) method is a time-dependent formulation of quantum chemistry, whereby the nuclear dynamics and electronic structure problems are solved simultaneously. Quantum mechanical effects in the nuclear dynamics are included, especially the nonadiabatic effects which are crucial in modeling dynamics on multiple electronic states. The AIMS method makes it possible to describe photochemistry from first principles molecular dynamics, with no empirical parameters. We describe the method and present the application to two molecules of interest in organic photochemistry-ethylene and cyclobutene. We show that the photodynamics of ethylene involves both covalent and ionic electronic excited states and the return to the ground state proceeds through a pyramidalized geometry. For the photoinduced ring opening of cyclobutene, we show that the disrotatory motion predicted by the Woodward-Hoffmann rules is established within the first 50 fs after optical excitation.