The heat- and odour-producing genus Arum (Araceae) has interested scientists for centuries. This long-term interest has allowed a deep knowledge of some complex processes, such as the physiology and dynamics of its characteristic lure-and-trap pollination system, to be built up. However, mainly because of its large distributional range and high degree of morphological variation, species' limits and relationships are still under discussion. Today, the genus comprises 28 species subdivided into two subgenera, two sections and six subsections. In this study, the phylogeny of the genus is inferred on the basis of four plastid regions, and the evolution of several morphological characters is investigated. Our phylogenetic hypothesis is not in agreement with the current infrageneric classification of the genus and challenges the monophyly of several species. This demonstrates the need for a new infrageneric classification based on characters reflecting the evolution of this enigmatic genus. To investigate the biogeography of Arum deeply, further spatiotemporal analyses were performed, addressing the importance of the Mediterranean basin in the diversification of Arum. Our results suggest that its centre of origin was the European–Aegean region, and that major diversification happened during the last 10 Myr. © 2010 The Linnean Society of London, Botanical Journal of the Linnean Society, 2010, 163, 14–32.