Natural compounds containing nitrogen are a source of many biologically active molecules used as drugs. Due to their multidirectional effects, they represent effective therapeutic compounds in many medical areas. Flavonoids, as well as their bioprecursors, chalcones, that occur in plants possess a number of medicinal benefits. Their synthetic amino derivatives constitute a large group of compounds that exhibit pharmacological activity. Due to the increasing level of drug resistance among patients, new therapeutic agents and options are urgently needed. Therefore, aminoflavonoids may be a promising source of new drugs. In this review, the biological activities of flavonoids, including chalcones, with complexes containing a nitrogen atom and the aminoflavones Ru and Pt are summarized. The purpose of this review is to provide an overview of the synthesis and pharmacological activity of aminoflavonoids and to show how synthetic modifications of these compounds can influence their biological activities. It covers the most recent reports on obtaining aminoflavones, aminochalcones, and their derivatives, along with information about their anticancer, antimicrobial, antimalarial, antiviral, and anti-inflammatory activities.