Psychosocial stress, and within the neuroendocrine reaction to stress specifically the glucocorticoid hormones, are well-characterized inhibitors of neural stem/progenitor cell proliferation in the adult hippocampus, resulting in a marked reduction in the production of new neurons in this brain area relevant for learning and memory. However, the mechanisms by which stress, and particularly glucocorticoids, inhibit neural stem/progenitor cell proliferation remain unclear and under debate. Here we review the literature on the topic and discuss the evidence for direct and indirect effects of glucocorticoids on neural stem/progenitor cell proliferation and adult neurogenesis. Further, we discuss the hypothesis that glucocorticoid rhythmicity and oscillations originating from the activity of the hypothalamus-pituitary-adrenal axis, may be crucial for the regulation of neural stem/progenitor cells in the hippocampus, as well as the implications of this hypothesis for pathophysiological conditions in which glucocorticoid oscillations are affected.