Coronavirus Disease-2019 (COVID-19) is an infectious disease caused by the SARS-CoV-2 virus. It was first identified in Wuhan, China, and has since spread causing a global pandemic. Various studies have been performed to understand the molecular mechanisms of viral infection for predicting drug repurposing candidates. However, such information is spread across many publications and it is very time-consuming to access, integrate, explore, and exploit. We developed CoVex, the first interactive online platform for SARS-CoV-2 and SARS-CoV-1 host interactome exploration and drug (target) identification. CoVex integrates 1) experimentally validated virus-human protein interactions, 2) human protein-protein interactions and 3) drug-target interactions. The web interface allows user-friendly visual exploration of the virus-host interactome and implements systems medicine algorithms for network-based prediction of drugs. Thus, CoVex is an important resource, not only to understand the molecular mechanisms involved in SARS-CoV-2 and SARS-CoV-1 pathogenicity, but also in clinical research for the identification and prioritization of candidate therapeutics. We apply CoVex to investigate recent hypotheses on a systems biology level and to systematically explore the molecular mechanisms driving the virus life cycle. Furthermore, we extract and discuss drug repurposing candidates involved in these mechanisms. CoVex renders COVID-19 drug research systems-medicine-ready by giving the scientific community direct access to network medicine algorithms integrating virus-host-drug interactions. It is available at https://exbio.wzw.tum.de/covex/.