Complex multicellular organisms have evolved specific mechanisms to replenish cells in homeostasis and during repair. Here, we discuss how emerging technologies (e.g., single-cell RNA sequencing) challenge the concept that tissue renewal is fueled by unidirectional differentiation from a resident stem cell. We now understand that cell plasticity, i.e., cells adaptively changing differentiation state or identity, is a central tissue renewal mechanism. For example, mature cells can access an evolutionarily conserved program (paligenosis) to reenter the cell cycle and regenerate damaged tissue. Most tissues lack dedicated stem cells and rely on plasticity to regenerate lost cells. Plasticity benefits multicellular organisms, yet it also carries risks. For one, when long-lived cells undergo paligenotic, cyclical proliferation and redifferentiation, they can accumulate and propagate acquired mutations that activate oncogenes and increase the potential for developing cancer. Lastly, we propose a new framework for classifying patterns of cell proliferation in homeostasis and regeneration, with stem cells representing just one of the diverse methods that adult tissues employ. Expected final online publication date for the Annual Review of Physiology, Volume 84 is February 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.