Activation of the tumour suppressor p53 upon cellular stress can induce a number of different cellular processes. The diverse actions of these processes are critical for the protective function of p53 in preventing the development of cancer. However, it is still not fully understood which process(es) activated by p53 is/are critical for tumour suppression and how this might differ depending on the type of cells undergoing neoplastic transformation and the nature of the drivers of oncogenesis. Moreover, it is not clear why upon activation of p53 some cells undergo cell cycle arrest and senescence whereas others die by apoptosis. Here we discuss some of the cellular processes that are crucial for p53-mediated tumour suppression and the factors that could impact cell fate upon p53 activation. Finally, we describe therapies aimed either at activating wild-type p53 or at changing the behaviour of mutant p53 to unleash tumour growth suppressive processes for therapeutic benefit in malignant disease.