The binding of transition metal compounds to nucleic acids is discussed in the perspectives of kinetics and their anticancer activity. Kinetics of ligand exchange is primarily determined by the intrinsic properties of the metal ions, and to a lesser degree by the ligands coordinated already to the metal ion. Metal compounds having ligand-exchange rates of the same order of magnitude as cell-division processes, e.g. many Pt(II), Ru(II) and Ru(III) compounds, are in use as chemotherapeutic drugs. Detailed knowledge of ligand exchange in such compounds is important for design of derivative and entirely new compounds. Metal coordination compounds of metal ions with much faster ligand-exchange reactions interact with DNA in a quite different way, namely primarily by compensation of negative charge of the polyanionic chain and are usually not active as anticancer agents. Examples of our recent work are presented in relation with experiments performed by others on new generations of platinum anti-cancer drugs.