Recoil-ion and electron momentum spectroscopy is a rapidly developing technique that allows one to measure the vector momenta of several ions and electrons resulting from atomic or molecular fragmentation. In a unique combination, large solid angles close to π Microccopes -the "bubble chambers of atomic physics" -mark the decisive step forward to investigate many-particle quantum-dynamics occurring when atomic and molecular systems or even surfaces and solids are exposed to time-dependent external electromagnetic fields.The present review concentrates on just these latest technical developments and on at least four new classes of fragmentation experiments that have emerged within about the last five years. First, multi-dimensional images in momentum space brought unprecedented information on the dynamics of single-photon induced fragmentation of fixed-in-space molecules and on their structure. Second, a break-through in the investigation of highintensity short-pulse laser induced fragmentation of atoms and molecules has been achieved by using Reaction Microccopes. Third, for electron and ion-impact, the investigation of twoelectron reactions has matured to a state such that first fully differential cross sections (FDCS) are reported. Forth, comprehensive sets of FDCS for single ionisation of atoms by ion-impact, the most basic atomic fragmentation reaction, brought new insight, a couple of surprises and unexpected challenges to theory at keV to GeV collision energies. In addition, a brief summary on the kinematics is provided at the beginning. Finally, the rich future potential of the method is shortly envisaged.2