Cell competition leads to elimination of a viable cell population, by fitter cells. Despite over forty years of research, the molecular mechanisms of competition in mammals are poorly understood. During my PhD I have investigated the mechanisms of competition by exploring an established mammalian cell culture system, in which wild-type MDCK cells eliminate scribble-deficient cells, and I have also developed a novel cell culture system to model mammalian competition. My work contributed to the discovery that scribble-deficient cells are eliminated not by biochemical exchange among cells, but by mechanical compaction. We termed this phenomenon mechanical competition. I employed transcriptional profiling to determine the molecular signature of mechanical losers, and identified activation of p53 signalling as their hallmark. My colleagues and I then demonstrated that elevation of p53 is both necessary and sufficient to trigger mechanical competition. In further investigating the mechanisms of mechanical competition, I found that compaction activates ROCK in scribble-deficient cells, and that this is required for their elimination. Inhibition of Src signalling in mechanical losers also protected them form out-competition, and integrin signalling is another pathway likely involved in mechanical competition. While investigating p53 competition, we observed that p53-high and p53-low cells engage in directional migration, with p53-high cells always at the migrating front. As a side-project, I investigated the role of p53 in directional migration, by exploring an established model with a single leader cell and multiple followers. We established a method to generate multinucleated leaders on demand. By creating leaders from p53-deficient cells, I established that p53 signalling is required for some, but not all multinucleated cells to trigger collective migration, thus implicating p53 signalling in a type of migration involved in wound healing. Finally, I successfully modelled p53-driven mechanical competition in a differentiated primary tracheal epithelial cell culture, thereby establishing a novel system to study mammalian competition, and also proving that p53 competition is conserved between different mammalian epithelia. Considering the involvement of p53, mechanical competition may play a major role in cancer.