To improve the discovery of more effective and less toxic pharmaceutical agents, large virtual repositories of synthesizable molecules have been generated to increase the explored chemicalpharmacological space diversity. Such libraries include billions of structural formulae of druglike molecules associated with data on synthetic schemes, required building blocks, estimated physical-chemical parameters, etc. Clearly, such repositories are "Big Data". Thus, to identify the most promising compounds with the required pharmacological properties (hits) among billions of available opportunities, special computational methods are necessary. We have proposed using a combined computational approach, which combines structural similarity assessment, machine learning, and molecular modeling. Our approach has been validated in a project aimed at finding new pharmaceutical agents against HIV/AIDS and associated comorbidities from the Synthetically Accessible Virtual Inventory (SAVI), a 1.75 billion compound database. Potential inhibitors of HIV-1 protease and reverse transcriptase and agonists of toll-like receptors and STING, affecting innate immunity, were computationally identified. The activity of the three synthesized compounds has been confirmed in a cell-based assay. These compounds belong to the chemical classes, in which the agonistic effect on TLR 7/8 had not been previously shown. Synthesis and biological testing of several dozens of compounds with predicted antiretroviral activity are currently taking place at the NCI/NIH. We also carried out virtual screening among one billion substances to find compounds potentially possessing anti-SARS-CoV-2 activity. The selected hits' information has been accepted by the European Initiative "JEDI Grand Challenge against COVID-19" for synthesis and further biological evaluation. The possibilities and limitations of the approach are discussed.