The placenta is an ephemeral organ containing diverse populations of trophoblasts that are all derived from the embryonic trophectoderm but have morphological, functional, and molecular diversity within and across species. In hemochorial placentation, these cells play especially important roles, interfacing with and modifying the cells of the maternal decidua. Within the rapidly growing placenta, it has been shown that there are trophoblast stem cells well characterized in the mouse and postulated but not well understood in primates. This review will discuss the characteristics of candidates for human and nonhuman primate trophoblast stem cells, present the diverse methods of their generation, and propose future prospects for experimental systems in which they can shed light on developmental and pathophysiological processes in human pregnancy.