Adult tissue-derived organoids allow for the expansion and maintenance of primary epithelial cells in a near-native state. These 3D and self-organizing organotypic cultures derived from adult tissues have been increasingly used in fundamental and translational research. A key feature of this organoid system is that it recapitulates the stem cell lineage and thus, the differentiated cell-type heterogeneity of the in vivo tissue of origin. Importantly, we and others have shown that organoids can be manipulated to expand different cell lineages, allowing for the study of rare cell types that would otherwise be very difficult to analyze. Here, focusing specifically on organoids of the small intestine, we discuss recent advances and future directions of this new avenue of organoid research. We highlight methods used to enrich specific cell types including stem cells, enterocytes, Paneth cells, goblet cells, micro-fold (M)-cells, tuft cells, and enteroendocrine cells (EECs) in intestinal organoids and focus on what each of these methods has taught us about the differentiation of adult intestinal stem cells (ISCs) to specific cell fates.