Intersystem crossing (ISC), formally forbidden within nonrelativistic quantum theory, is the mechanism by which a molecule changes its spin state. It plays an important role in the excited state decay dynamics of many molecular systems and not just those containing heavy elements. In the simplest case, ISC is driven by direct spin-orbit coupling between two states of different multiplicities. This coupling is usually assumed to remain unchanged by vibrational motion. It is also often presumed that spin-allowed radiationless transitions, i.e. internal conversion, and the nonadiabatic coupling that drives them, can be considered separately from ISC and spin-orbit coupling owing to the vastly different time scales upon which these processes are assumed to occur. However, these assumptions are too restrictive. Indeed, the strong mixing brought about by the simultaneous presence of nonadiabatic and spin-orbit coupling means that often the spin, electronic, and vibrational dynamics cannot be described independently. Instead of considering a simple ladder of states, as depicted in a Jablonski diagram, one must consider the more complicated spin-vibronic levels. Despite the basic ideas being outlined in the 1960s, it is only with the advent of high-level theory and femtosecond spectroscopy that the importance of the spin-vibronic mechanism for ISC in both fundamental as well as applied research fields has been revealed with significant impact across chemistry, physics, and biology. In this review article, we present the theory and fundamental principles of the spin-vibronic mechanism for ISC. This is followed by empirical rules to estimate the rate of ISC within this regime. The most recent developments in experimental techniques, theoretical methods, and models for the spin-vibronic mechanism are discussed. These concepts are subsequently illustrated with examples, including the ISC mechanisms in transition metal complexes, small organic molecules, and organic chromophores.