SARS-CoV-2 infection in the neonatal period poses previously unmet challenges to obstetricians and neonatologists, but several key questions are yet to be answered. Few cases of presumed in utero vertical transmission of the virus from infected mothers to fetuses have been reported, but stronger evidence is needed, from larger datasets with multiple biospecimens rigorously analyzed. Whether acquired before or after birth, SARS-CoV-2 infection in neonates can be symptomatic, but our comprehension of neonatal immune response and the subsequent clinical characteristics of COVID-19 in early life are incomplete. Finally, the pandemic challenged several dogmas regarding the management of mother-infant dyads, and again more robust data are needed to support the formulation of evidence-based guidelines. Here, we briefly summarize existing evidence and key unresolved questions about SARS-CoV-2 infection and COVID-19 in the neonatal period.