Alocasia comprises over 113 species of rainforest understorey plants in Southeast Asia, the Malesian region, and Australia. Several species, including giant taro, Alocasia macrorrhizos, and Chinese taro, Alocasia cucullata, are important food plants or ornamentals. We investigated the biogeography of this genus using plastid and nuclear DNA sequences (5200 nucleotides) from 78 accessions representing 71 species, plus 25 species representing 16 genera of the Pistia clade to which Alocasia belongs. Divergence times were inferred under strict and relaxed clock models, and ancestral areas with Bayesian and maximum likelihood approaches. Alocasia is monophyletic and sister to Colocasiagigantea from the SE Asian mainland, whereas the type species of Colocasia groups with Steudnera and Remusatia, requiring taxonomic realignments. Nuclear and plastid trees show topological conflict, with the nuclear tree reflecting morphological similarities, the plastid tree species' geographic proximity, suggesting chloroplast capture. The ancestor of Alocasia diverged from its mainland sister group c. 24 million years ago, and Borneo then played a central role in the expansion of Alocasia: 11-13 of 18-19 inferred dispersal events originated on Borneo. The Philippines were reached from Borneo 4-5 times in the Late Miocene and Early Pliocene, and the Asian mainland 6-7 times in the Pliocene. Domesticated giant taro originated on the Philippines, Chinese taro on the Asian mainland.