Development of drug delivery systems based on branched biocompatible polymers is one of the most promising areas of modern nanopharmaceutics. Researchers have been exploring this area several decades now, and the results of their efforts quickly find their way into production. Dendrimers, a new class of universal synthetic polymers with a highly functional surface, have a number of unique properties: constant size, high degree of branching, multivalence, solubility in water, definite molecular weight, internal cavities. With the release of VivaSol gel, the first dendrimer-based commercialized product, the "model range" of dendrimer carriers has grown significantly. Poly(amide-amine) (PAMAM) dendrimers, which consist of an alkyldiamine core and tertiary amine branches, are believed to be among the most promising compounds that can be used in the development of the new generation drugs. However, they were kept out of the list of clinically acceptable compounds for a long time because of their toxicity, unclear behavior in living systems and pharmacokinetic profile, as well the difficulties associated with establishing a therapeutic dose. This review presents basic information about PAMAM dendrimers and attempts to assess the prospects of their application in treatment of various diseases, including COVID-19.