We use a relatively densely sampled phylogeny to obtain preliminary estimates for the ages of the major clades identified in Euphorbia, with which we show that the succulent species of Euphorbia have diversified over the last 36 million years into many of the semi–arid, tropical parts of the world. Many major clades have subclades from widely separated regions, often on different continents. Our results imply that these distributions arose by long–distance dispersal after the break–up of Gondwana. In the case of Indian/South–east Asian succulents there appears to have been a single, relatively recent dispersal event from Africa. We have included many species from the Arabian Peninsula and Socotra and we show that these are nested within other, mainly African clades. In some cases Arabian and Socotran taxa have their closest relatives in adjacent parts of North–east Africa and most often this is true in recent clades, while in more ancient clades their closest relatives may be in Macaronesia or in the Namib Desert of Southern Africa so that these are typical 'Rand Flora' elements. In one case, closest known relatives are in North America. We find that Socotran taxa vary between 16 and 3 Ma old. The major diversifications of succulents in temperate Southern Africa (the crown clades in subg. Rhizanthium and more minor clades in subg. Chamaesyce) and in tropical East Africa (the crown clades in subg. Euphorbia) occurred in the last 20–3 Ma. In the Greater Cape Flora of the western part of Southern Africa the diversity in Euphorbia is mainly derived from one lineage in subg. Rhizanthium and one in subg.Chamaesyce. In contrast the diversity of Euphorbia in the Arabian Peninsula is derived from the invasion (mainly from Africa) of many separate lineages. We show that large, succulent trees are only found in subg. Euphorbia and only occur in the Old World. Most of them fall within a single clade and have evolved relatively recently.