Copper-containing coordination compounds attract wide attention due to the redox activity and biogenicity of copper ions, providing multiple pathways of biological activity. The pharmacological properties of metal complexes can be fine-tuned by varying the nature of the ligand and donor atoms. Copper-containing coordination compounds are effective antitumor agents, constituting a less expensive and safer alternative to classical platinum-containing chemotherapy, and are also effective as antimicrobial, antituberculosis, antimalarial, antifugal, and anti-inflammatory drugs. 64Cu-labeled coordination compounds are promising PET imaging agents for diagnosing malignant pathologies, including head and neck cancer, as well as the hallmark of Alzheimer’s disease amyloid-β (Aβ). In this review article, we summarize different strategies for possible use of coordination compounds in the treatment and diagnosis of various diseases, and also various studies of the mechanisms of antitumor and antimicrobial action.