I review theoretical models for the evolution of supergenes in the cases of Batesian mimicry in butterflies, distylous plants and sex chromosomes. For each of these systems, I outline the genetic evidence that led to the proposal that they involve multiple genes that interact during ‘complex adaptations’, and at which the mutations involved are not unconditionally advantageous, but show advantages that trade‐off against some disadvantages. I describe recent molecular genetic studies of these systems and questions they raise about the evolution of suppressed recombination. Nonrecombining regions of sex chromosomes have long been known, but it is not yet fully understood why recombination suppression repeatedly evolved in systems in distantly related taxa, but does not always evolve. Recent studies of distylous plants are tending to support the existence of recombination‐suppressed genome regions, which may include modest numbers of genes and resemble recently evolved sex‐linked regions. For Batesian mimicry, however, molecular genetic work in two butterfly species suggests a new supergene scenario, with a single gene mutating to produce initial adaptive phenotypes, perhaps followed by modifiers specifically refining and perfecting the new phenotype.