Although approximately 150 years have passed since the publication of On the origin of species by means of natural selection, the definition of what species are and the ways in which species originate remain contentious issues in evolutionary biology. The biological species concept, which defines species as groups of interbreeding natural populations that are reproductively isolated from other such groups, continues to draw support. However, there is a growing realization that many animal and plant species can hybridize with their close relatives and exchange genes without losing their identity. On occasion, such hybridization can lead to the origin of new species. A key to understanding what species are and the ways in which they originate rests to a large extent on a detailed knowledge of the nature and genetics of factors that limit gene flow between species and the conditions under which such isolation originates. The collection of papers in this issue addresses these topics and deals as well with some specific issues of hybrid speciation and the causes of species radiations. The papers included arise from a 1-day symposium on speciation held during the Sixth Biennial Meeting of the Systematics Association at Edinburgh in August 2007. In this introduction, we provide some background to these papers and highlight some key points made. The papers make clear that highly significant advances to our understanding of animal and plant speciation are currently being made across the range of this topic.