The placenta is essential for normal in utero development in mammals. In humans, defective placental formation underpins common pregnancy disorders such as pre-eclampsia and fetal growth restriction. The great variation in placental types across mammals means that animal models have been of limited use in understanding human placental development. However, new tools for studying human placental development, including 3D organoids, stem cell culture systems and single cell RNA sequencing, have brought new insights into this field. Here, we review the morphological, molecular and functional aspects of human placental formation, with a focus on the defining cell of the placenta - the trophoblast.