This review article focuses on the understanding of intersystem crossing (ISC) in molecules. It addresses readers who are interested in the phenomenon of intercombination transitions between states of different electron spin multiplicities but are not familiar with relativistic quantum chemistry. Among the spin-dependent interaction terms that enable a crossover between states of different electron spin multiplicities, spin-orbit coupling (SOC) is by far the most important. If SOC is small or vanishes by symmetry, ISC can proceed by electronic spin-spin coupling (SSC) or hyperfine interaction (HFI). Although this review discusses SSC- and HFI-based ISC, the emphasis is on SOC-based ISC. In addition to laying the theoretical foundations for the understanding of ISC, the review elaborates on the qualitative rules for estimating transition probabilities. Research on the mechanisms of ISC has experienced a major revival in recent years owing to its importance in organic light-emitting diodes (OLEDs). Exemplified by challenging case studies, chemical substitution and solvent environment effects are discussed with the aim of helping the reader to understand and thereby get a handle on the factors that steer the efficiency of ISC.