The intestinal epithelium constitutes the barrier between the gut lumen and the rest of the body and a very actively renewing cell population. The crypt/villus and crypt/cuff units of the mouse small intestine and colon are its basic functional units. The field is confronted with competing concepts with regard to the nature of the cells that are responsible for all the day-to day cell replacement and those that act to regenerate the tissue upon injury and with two diametrically opposed models for lineage specification. The review revisits groundbreaking pioneering studies to provide non expert readers and crypt watchers with a factual analysis of the origins of the current models deduced from the latest spectacular advances. It also discusses recent progress made by addressing these issues in the crypts of the colon, which need to be better understood, since they are the preferred sites of major pathologies.