In this paper, we briefly review a series of recent pioneering experiments on few-photon-induced multiple fragmentation of atoms and molecules performed at the free electron laser (FEL) at Hamburg (FLASH) using a ‘reaction microscope’, i.e. a coincident momentum imaging technique. For atoms we consider the most basic nonlinear process, namely direct or sequential two-photon double ionization (TPDI). In particular, benchmark data for theory are presented, such as recoil–ion momentum distributions for direct TPDI of He and Ne, and fully differential data for sequential TPDI of Ne. For molecules we show how one can identify contributions from different reaction channels by inspecting the measured kinetic energy and angular distributions of ionic fragments and even infer the time delay between the two-photon absorption events in TPDI by detailed comparison with theory. Finally, we describe a novel split mirror arrangement for EUV-pump–EUV-probe experiments and present the very first time-resolved data on the dynamics of N2 molecules irradiated by the FLASH light.