This review examines the existing knowledge about Ru(II)/(III) ion complexes with a potential application in medicine or pharmacy, which may offer greater potential in cancer chemotherapy than Pt(II) complexes, which are known to cause many side effects. Hence, much attention has been paid to research on cancer cell lines and clinical trials have been undertaken on ruthenium complexes. In addition to their antitumor activity, ruthenium complexes are under evaluation for other diseases, such as type 2 diabetes, Alzheimer’s disease and HIV. Attempts are also being made to evaluate ruthenium complexes as potential photosensitizers with polypyridine ligands for use in cancer chemotherapy. The review also briefly examines theoretical approaches to studying the interactions of Ru(II)/Ru(III) complexes with biological receptors, which can facilitate the rational design of ruthenium-based drugs.