The COVID-19 pandemic has caused millions of deaths and massive societal distress worldwide. Therapeutic solutions are urgently needed but de novo drug development remains a lengthy process. One promising alternative is computational drug repurposing, which enables the prioritization of existing compounds through fast in silico analyses. Recent efforts based on molecular docking, machine learning, and network analysis have produced actionable predictions. Some predicted drugs, targeting viral proteins and pathological host pathways are undergoing clinical trials. Here, we review this work, highlight drugs with high predicted efficacy and classify their mechanisms of action. We discuss the strengths and limitations of the published methodologies and outline possible future directions. Finally, we curate a list of COVID-19 data portals and other repositories that could be used to accelerate future research.