Activation of the p53 signaling pathway by DNA‐damaging agents was originally proposed to result either in cell cycle checkpoint activation to promote survival or in apoptotic cell death. This model provided the impetus for numerous studies focusing on the development of p53‐based cancer therapies. According to recent evidence, however, most p53 wild‐type human cell types respond to ionizing radiation by undergoing stress‐induced premature senescence (SIPS) and not apoptosis. SIPS is a sustained growth‐arrested state in which cells remain viable and secrete factors that may promote cancer growth and progression. The p21^WAF1 (hereafter p21) protein has emerged as a key player in the p53 pathway. In addition to its well‐studied role in cell cycle checkpoints, p21 regulates p53 and its upstream kinase (ATM), controls gene expression, suppresses apoptosis, and induces SIPS. Herein, we review these and related findings with human solid tumor‐derived cell lines, report new data demonstrating dynamic behaviors of p53 and p21 in the DNA damage response, and examine the gain‐of‐function properties of cancer‐associated p53 mutations. We point out obstacles in cancer‐therapeutic strategies that are aimed at reactivating the wild‐type p53 function and highlight some alternative approaches that target the apoptotic threshold in cancer cells with differing p53 status.