The effect of SARS-CoV-2 infection on placental function is not well understood. Analysis of placentas from women who tested positive at delivery showed SARS-CoV-2 genomic and subgenomic RNA in 22 out of 52 placentas. Placentas from two mothers with symptomatic COVID-19 whose pregnancies resulted in adverse outcomes for the fetuses contained high levels of viral Alpha variant RNA. The RNA was localized to the trophoblasts that cover the fetal chorionic villi in direct contact with maternal blood. The intervillous spaces and villi were infiltrated with maternal macrophages and T cells. Transcriptome analysis showed an increased expression of chemokines and pathways associated with viral infection and inflammation. Infection of placental cultures with live SARS-CoV-2 and spike protein-pseudotyped lentivirus showed infection of syncytiotrophoblast and, in rare cases, endothelial cells mediated by ACE2 and Neuropilin-1. Viruses with Alpha, Beta, and Delta variant spikes infected the placental cultures at significantly greater levels.