Cisplatin is one of the most important and widely used anticancer drug in clinical use. However, its effectiveness is limited by its high toxicity and incidence of drug resistance. This has provided motivation for the search for transition metal-based drugs with a wider spectrum of activity and lower systemic toxicities. Some of the recent successes are compounds based on the bis-am(m)ine platinum(IV) structure and ruthenium-based co-ordination compounds with N-heterocyclic ligands, and they are presently undergoing evaluation in clinical trials. Extending on these developments, novel platinum and ruthenium complexes designed to overcome drug resistance mechanisms were developed as part of the dissertation. The new compounds exploit passive and active targeting strategies to overcome aspects of drug resistance. The passive drug targeting strategies included enhancing the lipophilicity of drug and conjugating the transition metal-based drug to relevant biomolecules, with the aim of improving their accumulation in cancer cells and tumours. For active targeting, platinum and ruthenium complexes bearing glutathione-S-transferase (GST) inhibitor ligands were developed as multifuctional drugs that could also inhibit GST-activity, since this is correlated to drug resistance. In vitro techniques against a panel of established carcinoma cell lines were used to establish the efficacy of the complexes. In addition, the rationale and synthetic considerations for each of the design strategies are discussed.