Arboviruses (arthropod-borne viruses), though taxonomically diverse, share a cycle of transmission between vertebrate hosts and arthropod vectors. All but one arbovirus species belong to one of five families of RNA viruses, suggesting that the high mutation frequencies of RNA genomes may be a prerequisite for entry into a cycle of alternating replication in the very different environments represented by vertebrate and invertebrate animals. Arboviruses such as dengue, yellow fever, and Venezuelan equine encephalitis viruses pose significant, recognized threats to human and animal health. Moreover, the potential for new arboviruses to emerge from enzootic cycles to cause disease in humans and domestic animals, or for recognized arboviruses to spread into new geographic areas, is already high and may be exacerbated by ongoing changes in human demography and global climate. Thus it is critical to understand the forces that shape the evolution of arboviruses in order to better predict their emergence and to control their spread. In this chapter we review existing scholarship on the origin, diversification and evolution of host and vector use of arboviruses, with a focus on the two best-studied groups: the vector-borne alphaviviruses and flaviviruses. Specifically, we review the contribution of phylogenetic analysis to current understanding of arbovirus evolution and epidemiology, we evaluate the role of recombination and reassortment in the origin of new arboviruses, and we examine the mechanisms of arbovirus emergence and geographic spread. In addition, we discuss the impact of cycles of alternating replication in vertebrate hosts and vectors on the rates and patterns of arbovirus evolution and the selection imposed by alternating transmission cycles on specific arbovirus phenotypes. Finally we consider the challenges that arbovirus evolution may pose to the deployment of existing and novel measures for disease control.