Scientific research suggests that cacti evolved somewhere in the last 30 to 40 million years. A long time back the Americas were joined to other continents but after the continental drift became divided. Unique species of plants evolved in the New World and must have developed after the continents had moved apart, this occuring during the last 50 million years. This explains why cacti are so rare if existant at all on continents such as Africa as the continents had already divided when cacti evolved.
Many succulent plants such as the Euphorbias in both the Old and New World bear a striking resemblance to cacti, and are often wrongly called cactus. However none of these are closely related to the Cactaceae family.