In many non-mammalian organisms, a population of germ-line stem cells supports continuing production of gametes during post-natal life, and germ-line stem cells are also present and functional in male mammals. Traditionally, however, they have been thought not to exist in female mammals, who instead generate all their germ cells during fetal life. Over the last several years, this dogma has been challenged by several reports, while being supported by others. We describe and compare these conflicting studies with the aim of understanding how they came to opposing conclusions. We first consider studies that, by examining marker-gene expression, the fate of genetically marked cells, and consequences of depleting the oocyte population, addressed whether ovaries of post-natal females contain oogonial stem cells that give rise to new oocytes. We next discuss whether ovaries contain cells that, even if inactive under physiological conditions, nonetheless possess oogonial stem cell properties that can be revealed through cell culture. We then examine studies of whether cells harvested after long-term culture of cells obtained from ovaries can, following transplantation into ovaries of recipient females, give rise to oocytes and offspring. Finally, we note studies where somatic cells have been re-programmed to acquire a female germ-cell fate. We conclude that the weight of evidence strongly supports the traditional interpretation that germ-line stem cells do not exist post-natally in female mammals. However, the ability to generate germ cells from somatic cells in vitro establishes a method to generate new gametes from cells of post-natal mammalian females.