Research into Heliconius butterflies has made a significant contribution to evolutionary biology. Here, we review our understanding of the diversification of these butterflies, covering recent advances and a vast foundation of earlier work. Whereas no single group of organisms can be sufficient for understanding life's diversity, after years of intensive study, research into Heliconius has addressed a wide variety of evolutionary questions. We first discuss evidence for widespread gene flow between Heliconius species and what this reveals about the nature of species. We then address the evolution and diversity of warning patterns, both as the target of selection and with respect to their underlying genetic basis. The identification of major genes involved in mimetic shifts, and homology at these loci between distantly related taxa, has revealed a surprising predictability in the genetic basis of evolution. In the final sections, we consider the evolution of warning patterns, and Heliconius diversity more generally, within a broader context of ecological and sexual selection. We consider how different traits and modes of selection can interact and influence the evolution of reproductive isolation.