Biogeography is the discipline of biology that studies the present and past distribution patterns of biological diversity and their underlying environmental and historical causes. For most of its history, biogeography has been divided into proponents of vicariance explanations, who defend that distribution patterns can mainly be explained by geological, tectonic-isolating events; and dispersalists, who argue that current distribution patterns are largely the result of recent migration events. This paper provides an overview of the evolution of the discipline from methods focused on finding general patterns of distribution (cladistic biogeography), to those that integrate biogeographic processes (event-based biogeography), to modern probabilistic approaches (parametric biogeography). The latter allows incorporating into biogeographic inference estimates of the divergence time between lineages (usually based on DNA sequences) and external sources of evidence, such as information on past climate and geography, the organism fossil record, or its ecological tolerance. This has revolutionized the discipline, allowing it to escape the dispersal versus vicariance dilemma and to address a wider range of evolutionary questions, including the role of ecological and historical factors in the construction of biomes or the existence of contrasting patterns of range evolution in animals and plants.