The tumor suppressor protein p53 is inactivated by mutation in about half of all human cancers. Most mutations are located in the DNA-binding domain of the protein. It is, therefore, important to understand the structure of p53 and how it responds to mutation, so as to predict the phenotypic response and cancer prognosis. In this review, we present recent structural and systematic functional data that elucidate the molecular basis of how p53 is inactivated by different types of cancer mutation. Intriguingly, common cancer mutants exhibit a variety of distinct local structural changes, while the overall structural scaffold is largely preserved. The diverse structural and energetic response to mutation determines: (i) the folding state of a particular mutant under physiological conditions; (ii) its affinity for the various p53 target DNA sequences; and (iii) its protein-protein interactions both within the p53 tetramer and with a multitude of regulatory proteins. Further, the structural details of individual mutants provide the basis for the design of specific and generic drugs for cancer therapy purposes. In combination with studies on second-site suppressor mutations, it appears that some mutants are ideal rescue candidates, whereas for others simple pharmacological rescue by small molecule drugs may not be successful.