Renewal of the intestinal epithelium occurs approximately every week and requires a careful balance between cell proliferation and differentiation to maintain proper lineage ratios and support absorptive, secretory, and barrier functions. We review models used to study the mechanisms by which intestinal stem cells (ISCs) fuel the rapid turnover of the epithelium during homeostasis and might support epithelial regeneration after injury. In anatomically defined zones of the crypt stem cell niche, phenotypically distinct active and reserve ISC populations are believed to support homeostatic epithelial renewal and injury-induced regeneration, respectively. However, other cell types previously thought to be committed to differentiated states might also have ISC activity and participate in regeneration. Efforts are underway to reconcile the proposed relatively strict hierarchical relationships between reserve and active ISC pools and their differentiated progeny; findings from models provide evidence for phenotypic plasticity that is common among many if not all crypt-resident intestinal epithelial cells. We discuss the challenges to consensus on ISC nomenclature, technical considerations, and limitations inherent to methodologies used to define reserve ISCs, and the need for standardized metrics to quantify and compare the relative contributions of different epithelial cell types to homeostatic turnover and post-injury regeneration. Increasing our understanding of the high-resolution genetic and epigenetic mechanisms that regulate reserve ISC function and cell plasticity will help refine these models and could affect approaches to promote tissue regeneration after intestinal injury.