The history of the genus Babesia is briefly outlined. The classical differences with the main other genus of non-pigment-forming hemoparasites, Theileria, are the absence of extra-erythrocytic multiplication (schizogony) in Babesia and the cycle in the vector tick, which includes transovarial transmission in Babesia but only transstadial transmission in Theileria. Also, the multiplication in the red cell of Babesia, by budding, most often results in two daughter cells (merozoites), while that of Theileria gives four merozoites, often as a Maltese cross. In particular this means that what is still commonly called Babesia microti is not a Babesia and that it would be just as logical to speak of human theileriosis as of babesiosis. The small piroplasm of horses, long known as Babesia equi, is already commonly designated as Theileria equi. However, on molecular grounds, it may be necessary to create a new genus for these parasites. The Babesia species of domestic animals are briefly discussed and presented in a table.