In this chapter, I discuss the processes that contribute to the breakdown of hybridisation between populations, eventually leading to the emergence of new species in the Tree of Life. The chapter begins by introducing the Biological Species Concept and discusses some of the challenges involved in defining species. Drawing on various examples, I explore different reasons why mating between incipient species might fail or, alternatively, how it might result in hybrid offspring that fail to survive or reproduce. I also discuss how factors such as geographic isolation and ecological specialisation can facilitate speciation. The chapter illustrates how our current understanding of speciation relies on different kinds of evidence emerging from field studies, genomics and theoretical models.