The tumour suppressor gene TP53 is mutated in ~50% of human cancers. In addition to its function in tumour suppression, p53 also plays a major role in the response of malignant as well as nontransformed cells to many anticancer therapeutics, particularly those that cause DNA damage. P53 forms a homotetrameric transcription factor that is reported to directly regulate ~500 target genes, thereby controlling a broad range of cellular processes, including cell cycle arrest, cell senescence, DNA repair, metabolic adaptation and cell death. For a long time, induction of apoptotic death in nascent neoplastic cells was regarded as the principal mechanism by which p53 prevents tumour development. This concept has, however, recently been challenged by the findings that in striking contrast to Trp53-deficient mice, gene-targeted mice that lack the critical effectors of p53-induced apoptosis do not develop tumours spontaneously. Remarkably, even mice lacking all mediators critical for p53-induced apoptosis, G1/S boundary cell cycle arrest and cell senescence do not develop any tumours spontaneously. In this review we discuss current understanding of the mechanisms by which p53 induces cell death and how this affects p53-mediated tumour suppression and the response of malignant cells to anticancer therapy.