The human placenta is a poorly-understood organ, but one that is critical for proper development and growth of the fetus in-utero. The epithelial cell type that contributes to primary placental functions is called "trophoblast," including two main subtypes, villous and extravillous trophoblast. Cytotrophoblast and syncytiotrophoblast comprise the villous compartment and contribute to gas and nutrient exchange, while extravillous trophoblast invade and remodel the uterine wall and vessels, in order to supply maternal blood to the growing fetus. Abnormal differentiation of trophoblast contributes to placental dysfunction and is associated with complications of pregnancy, including preeclampsia (PE) and fetal growth restriction (FGR). This review describes what is known about the cellular organization of the placenta during both normal development and in the setting of PE/FGR. It also explains known trophoblast lineage-specific markers and pathways regulating their differentiation, and how these are altered in the setting of PE/FGR, focusing on studies which have used human placental tissues. Finally, it also highlights remaining questions and needed resources to advance this field.