Background: The Greenland shark is renowned for its great longevity, yet little is known about its reproduction. Methods: We supplemented the sparse information on this species by extrapolation from observations on other members of the sleeper shark family and the order Squaliformes. Results and conclusion: The Greenland shark is viviparous and a single observation suggests a litter size of about ten. The gestation period is unknown, but embryos reach a length of around 40 cm at birth. Nutrition is derived from the yolk sac with minimal histotrophy. The surface area of the uterus is increased by villi that presumably increase in length with advancing gestation. These villi are not likely to be secretory but play a key role in the oxygen supply to the embryo. We argue that the ability of the uterus to supply oxygen is a limiting factor for litter size, which is not likely to exceed the small number reported in this and other sleeper sharks.