The field of organoid engineering promises to revolutionize medicine with wide‐ranging applications of scientific, engineering, and clinical interest, including precision and personalized medicine, gene editing, drug development, disease modelling, cellular therapy, and human development. Organoids are a three‐dimensional (3D) miniature representation of a target organ, are initiated with stem/progenitor cells, and are extremely promising tools with which to model organ function. The biological basis for organoids is that they foster stem cell self‐renewal, differentiation, and self‐organization, recapitulating 3D tissue structure or function better than two‐dimensional (2D) systems. In this review, we first discuss the importance of epithelial organs and the general properties of epithelial cells to provide a context and rationale for organoids of the liver, pancreas, and gall bladder. Next, we develop a general framework to understand self‐organization, tissue hierarchy, and organoid cultivation. For each of these areas, we provide a historical context, and review a wide range of both biological and mathematical perspectives that enhance understanding of organoids. Next, we review existing techniques and progress in hepatobiliary and pancreatic organoid engineering. To do this, we review organoids from primary tissues, cell lines, and stem cells, and introduce engineering studies when applicable. We discuss non‐invasive assessment of organoids, which can reveal the underlying biological mechanisms and enable improved assays for growth, metabolism, and function. Applications of organoids in cell therapy are also discussed. Taken together, we establish a broad scientific foundation for organoids and provide an in‐depth review of hepatic, biliary and pancreatic organoids. [ABSTRACT FROM AUTHOR]