Viviparity (live-birth) has evolved from oviparity (egg-laying) multiple times in sharks. While most transitions from oviparity to viviparity have resulted in non-placental forms of viviparity, some sharks develop a yolk sac placenta during pregnancy. The Australian sharpnose shark (Rhizoprionodon taylori) is a placental species that suspends embryonic development in a diapause for most of pregnancy. To identify structures involved in supporting rapid embryonic growth in late pregnancy, we examined uterine and placental morphology by light and electron microscopy. Paraplacental uterine regions have morphological specialisations consistent with secretion and fluid transport between uterine tissues and the lumen. Uterine secretions in the lumen may be absorbed by the outgrowths on the embryonic umbilical cord ('appendiculae'), which are densely covered by microvilli. The placenta consists of uterine villi that interdigitate with the yolk sac and enhance the surface area available for fetomaternal exchange. The yolk sac does not invade the uterine epithelium, and the egg capsule remains intact at the placental interface, separating maternal and fetal tissues. Some placental uterine epithelial cells are secretory, and endocytic vesicles in the opposing yolk sac ectodermal cells suggest that nutrient transport is by histotrophic uterine secretion followed by fetal absorption. Respiratory gases, water and possibly small nutrients likely diffuse across the placenta, where maternal and fetal blood vessels are ~2 μm apart. Placental structure in R. taylori is similar to most other sharks, but there are differences in cellular structures between species that may indicate species-specific placental transport mechanisms.