The present theoretical work deals with the emission of correlated electron-electron and electron-positron pairs from crystalline surfaces induced by the collision of a low-energy primary electron or positron with a valence electron. For short, these two processes are referred to as (e,2e) and (p,ep), respectively. In generalization of earlier theory, an (e,2e) formalism has been developed, which incorporates spin-orbit coupling and exchange in ferromagnets on an equal footing. The basic ingredients are single-particle states, which are solutions of a Dirac equation with an effective magnetic field. From these states, two-electron states are obtained, which are correlated by exchange and Coulomb interaction. The spin-dependent (e,2e) reaction cross section is then expressed as the transition probability between an initial and a final two-electron state. While of course already applicable to (e,2e) from nonmagnetic systems as a special case, the theory has been extended to handle positron-induced electron-positron emission (p,ep). The formalism was implemented in a computer code and numerical results were obtained for several selected crystalline surface systems. The quasiparticle potential input required for these computations was obtained by firstly performing, within density functional theory, an ab initio calculation of the ground state of the system and secondly augmenting the resulting real potential by a complex self-energy correction. This quasiparticle potential was also used to calculate spin- and layer-resolved densities of states (spectral functions), which are very valuable for the interpretation of the calculated pair emission spectra. A comparative study of (e,2e) and (p,ep) was carried out for the Cu(111) surface. As a consequence of the opposite sign of the Coulomb interaction, the most outstanding difference appears in angular distributions of the two emitted particles with equal energies. While for (e,2e) there is a central depletion zone (exchange-correlation hole), the (p,ep) distributions exhibit a central accumulation zone (correlation hill). At larger angles sharp features arise from single-particle surface resonances. In conjunction with experimental work at the Max-Planck-Institut für Mikrostrukturphysik in Halle, spin-dependent (e,2e) angular and energy distributions were calculated for the ferromagnetic Fe(001) surface. They are analyzed with the aid of the spin-, momentum-, symmetry- and layer-resolved valence electron density of states. The observed spectra are found to arise almost completely from only three surface-parallel atomic layers. Momentum distributions for parallel spins of the emitted electrons exhibit an exchange-correlation hole, which is larger than the correlation hole in the antiparallel spin case. By comparing experimental antiparallel-spin pair spectra with their theoretical counterparts an effective screening strength of the Coulomb interaction in the surface region is determined. A similar separation of Coulomb correlation and exchange effects in (e,2e) is possible, if the valence electron is in a recently discovered spin-polarized surface state on the nonmagnetic W(110) surface. Further, (e,2e) can achieve a spin-resolved mapping of the dispersion of this state with surface-parallel momentum. As a prototype case, for which spin-orbit coupling effects are comparable in size to magnetic exchange effects, the ferromagnetic surface system Co/W(110) has been chosen. (e,2e) spectra are presented together with the underlying spin- and layer-resolved valence electron spectral density. More detailed insight is provided by calculations, in which spin-orbit coupling was selectively switched off for the valence electron and for the primary and emitted electrons. The theoretical results are in overall agreement with experimental data. Furthermore, sizable magnetic dichroism is predicted.