The development of antiviral treatment and anticancer theragnostic agents in recent decades has been associated with nanotechnologies, and primarily with inorganic nanoparticles (INPs) of metal and metal oxides. The large specific surface area and its high activity make it easy to functionalize INPs with various coatings (to increase their stability and reduce toxicity), specific agents (allowing retention of INPs in the affected organ or tissue), and drug molecules (for antitumor and antiviral therapy). The ability of magnetic nanoparticles (MNPs) of iron oxides and ferrites to enhance proton relaxation in specific tissues and serve as magnetic resonance imaging contrast agents is one of the most promising applications of nanomedicine. Activation of MNPs during hyperthermia by an external alternating magnetic field is a promising method for targeted cancer therapy. As therapeutic tools, INPs are promising carriers for targeted delivery of pharmaceuticals (either anticancer or antiviral) via magnetic drug targeting (in case of MNPs), passive or active (by attaching high affinity ligands) targeting. The plasmonic properties of Au nanoparticles (NPs) and their application for plasmonic photothermal and photodynamic therapies have been extensively explored recently in tumor treatment. The Ag NPs alone and in combination with antiviral medicines reveal new possibilities in antiviral therapy. The prospects and possibilities of INPs in relation to magnetic hyperthermia, plasmonic photothermal and photodynamic therapies, magnetic resonance imaging, targeted delivery in the framework of antitumor theragnostic and antiviral therapy are presented in this review.