Tyrosyl-DNA phosphodiesterase 1 (Tdp1) is a recently discovered enzyme that catalyzes the hydrolysis of 3-phosphotyrosyl bonds. Such linkages form in vivo following the DNA processing activity of topoisomerase I (Top1). For this reason, Tdp1 has been implicated in the repair of irreversible Top1-DNA covalent complexes, which can be generated by either exogenous or endogenous factors. Tdp1 has been regarded as a potential therapeutic co-target of Top1 in that it seemingly counteracts the effects of Top1 inhibitors, such as camptothecin and its clinically used derivatives. Thus, by reducing the repair of Top1-DNA lesions, Tdp1 inhibitors have the potential to augment the anticancer activity of Top1 inhibitors provided there is a presence of genetic abnormalities related to DNA checkpoint and repair pathways. Human Tdp1 can also hydrolyze other 3-end DNA alterations including 3-phosphoglycolates and 3-abasic sites indicating it may function as a general 3-DNA phosphodiesterase and repair enzyme. The importance of Tdp1 in humans is highlighted by the observation that a recessive mutation in the human TDP1 gene is responsible for the inherited disorder, spinocerebellar ataxia with axonal neuropathy (SCAN1). This review provides a summary of the biochemical and cellular processes performed by Tdp1 as well as the rationale behind the development of Tdp1 inhibitors for anticancer therapy.