This review presents techniques for the computation of multi-electron integrals over Cartesian and solid-harmonic Gaussian-type orbitals as used in standard electronic-structure investigations. The review goes through the basics for one- and two-electron integrals, discuss details of various two-electron integral evaluation schemes, approximative methods, techniques to compute multi-electron integrals for explicitly correlated methods, and property integrals. © 2011 John Wiley & Sons, Ltd.