SARS-CoV-2 infection during pregnancy leads to an increased risk of adverse pregnancy outcomes. Although the placenta itself can be a target of virus infection, most neonates are virus free and are born healthy or recover quickly. Here, we investigated the impact of SARS-CoV-2 infection on the placenta from a cohort of women who were infected late during pregnancy and had tested positive for SARS-CoV-2 by qRT-PCR at delivery. SARS-CoV-2 genomic and subgenomic RNA was detected in 23 out of 55 placentas (41%). Three placentas with high virus content were obtained from mothers who presented with severe COVID-19 and whose pregnancies resulted in adverse outcomes for the fetuses, including intrauterine fetal demise, stillbirth, and a preterm delivered baby still in newborn intensive care. Examination of the placental samples with high virus content showed efficient SARS-CoV-2 infection, using RNA in situ hybridization to detect genomic and replicating viral RNA, and immunohistochemistry to detect SARS-CoV-2 nucleocapsid protein. Infection was restricted to syncytiotrophoblast cells that envelope the fetal chorionic villi and are in direct contact with maternal blood. The infected placentas displayed massive infiltration of maternal immune cells including macrophages into intervillous spaces, potentially contributing to inflammation of the tissue. Ex vivo infection of placental cultures with SARS-CoV-2 or with SARS-CoV-2 spike (S) protein pseudotyped lentivirus targeted mostly syncytiotrophoblast and, to a lesser extent, endothelial cells. Infection was reduced by using blocking antibodies against ACE2 and against Neuropilin 1, suggesting that SARS-CoV-2 may utilize alternative receptors for entry into placental cells.