I will discuss mathematical models of stem cell dynamics in tissues at homeostasis, focusing on the ability of negative feedback loops within cell lineages to contribute to homeostatic control. These dynamics will be examined both in non-spatial and spatially explicit computational models, highlighting how spatial interactions can change dynamics and conclusions. The talk will further discuss the evolution of cells towards escape from homeostatic control, which gives rise to cancerous growth of cells. In the cancer cell growth dynamics, the models will be used to examine factors that determine the fraction of cancer stem cells in tumors, which in turn can determine the degree to which tumors respond to chemotherapies. Higher stem cell fractions correlate with increased resistance to therapy. This theory will be applied to data from bladder cancer, with the aim to better understand the heterogeneity that is observed in the responses among different patients to treatments.