Modified polymeric gels, including nanogels, which play not only the role of a bioinert matrix, but also perform regulatory, catalytic, and transport functions due to the active fragments introduced into them, can significantly advance the solution to the problem of targeted drug delivery in an organism. This will significantly reduce the toxicity of used pharmaceuticals and expand the range of their therapeutic, diagnostic, and medical application. This review presents a comparative description of gels based on synthetic and natural polymers intended for pharmaceutical-targeted drug delivery in the field of therapy of inflammatory and infectious diseases, dentistry, ophthalmology, oncology, dermatology, rheumatology, neurology, and the treatment of intestinal diseases. An analysis was made of most actual sources published for 2021–2022. The review is focused on the comparative characteristics of polymer gels in terms of their toxicity to cells and the release rate of drugs from nano-sized hydrogel systems, which are crucial initial features for their further possible application in mentioned areas of biomedicine. Different proposed mechanisms of drug release from gels depending on their structure, composition, and application are summarized and presented. The review may be useful for medical professionals, and pharmacologists dealing with the development of novel drug delivery vehicles.