This contribution is devoted to the theory of ion-induced electron emission from solids, with the emphasis on bulk as opposed to surface processes. With the aim of describing yields and energy spectra of emitted electrons, we discuss pertinent elementary processes, l.e., primary and secondary excitation, electron transport, and escape. I'lith regard to the primary process, proper distinction is made between high-and low-velocity ions, and reference is made to the physics of ion-atom collisions as well as to dielectric stopping theory. The discussion of secondary excitation makes reference to the theory of ionization cascades as well as atomic recoil cascades. Electron transport is considered first in an infinite medium and subsequently, within the diffusion approximation, in a semi-infinite medium. Special attention is paid to pertinent electron mean free paths, inelastic processes being estimated on the basis of the free-electron-gas model of a solid. We find that the neglect of elastic scattering of electrons in most existing treatments of electron emission has severe consequences on the interpretation of structure in measured electron spectra. Comments are made on the escape depth of electrons.