Summary Orchids constitute one of the most spectacular radiations of flowering plants. However, their origin, spread across the globe, and hotspots of speciation remain uncertain due to the lack of an up‐to‐date phylogeographic analysis. We present a new Orchidaceae phylogeny based on combined high‐throughput and Sanger sequencing data, covering all five subfamilies, 17/22 tribes, 40/49 subtribes, 285/736 genera, and c. 7% (1921) of the 29 524 accepted species, and use it to infer geographic range evolution, diversity, and speciation patterns by adding curated geographical distributions from the World Checklist of Vascular Plants. The orchids' most recent common ancestor is inferred to have lived in Late Cretaceous Laurasia. The modern range of Apostasioideae, which comprises two genera with 16 species from India to northern Australia, is interpreted as relictual, similar to that of numerous other groups that went extinct at higher latitudes following the global climate cooling during the Oligocene. Despite their ancient origin, modern orchid species diversity mainly originated over the last 5 Ma, with the highest speciation rates in Panama and Costa Rica. These results alter our understanding of the geographic origin of orchids, previously proposed as Australian, and pinpoint Central America as a region of recent, explosive speciation.