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 modeling, cellular therapy, and a basic understanding of human development. Organoids are a three-dimensional (3D), miniature, caricature of a target organ, are initiated with stem/progenitor cells, and are extremely promising tools to model organ function. The biological basis for organoids is that they foster stem cell-self renewal, differentiation, and self-organization, recapitulating tissue structure or function better than 2D systems. In this review, we first discuss the importance of epithelial organs and the general properties of epithelial cells to provide context for the liver, pancreas, and gall bladder and rationale for organoid cultures. Next, we develop a general framework to understand self-organization, tissue hierarchy, and organoid cultivation. For each of these areas, we provide historical context, and review both a wide range of biological and/or biophysical/mathematic perspectives that enhances understanding of organoids. Next, we review existing techniques and progress in hepatobiliary and pancreatic organoid engineering. To do this, we review organoids from both primary tissues, cell lines, and stem cells, and introduce engineering studies when applicable. Noninvasive assessment of 1 organoids can reveal underlying biology and enable improved assays for growth, metabolism, and function. Applications of organoid for cell therapy are also discussed. Taken together, we establish a broad strong scientific foundation for organoids and provide an in-depth review of hepatic, biliary and pancreatic organoids.