The definition, regulation and function of intestinal stem cells (ISCs) has been hotly debated. Recent discoveries have started to clarify the nature of ISCs, but many questions remain. This review discusses the current advances and controversies of ISC biology as well as theoretical compartmental models that have been coupled with in vivo experimentation to investigate the mechanisms of ISC dynamics during homeostasis, tumorigenesis, repair and development. We conclude our review by discussing the key lingering questions in the field and proposing how many of these questions can be addressed using both compartmental models and experimental techniques.