The sudden outbreak and worldwide spread of the SARS-CoV-2 pandemic pushed the scientific community to find fast solutions to cope with the health emergency. COVID-19 complexity, in terms of clinical outcomes, severity, and response to therapy suggested the use of multifactorial strategies, characteristic of the network medicine, to approach the study of the pathobiology. Proteomics and interactomics especially allow to generate datasets that, reduced and represented in the forms of networks, can be analyzed with the tools of systems biology to unveil specific pathways central to virus–human host interaction. Moreover, artificial intelligence tools can be implemented for the identification of druggable targets and drug repurposing. In this review article, we provide an overview of the results obtained so far, from a systems biology perspective, in the understanding of COVID-19 pathobiology and virus–host interactions, and in the development of disease classifiers and tools for drug repurposing.