Three-dimensional models of organ biogenesis have recently flourished. They promote a balance between stem/progenitor cell expansion and differentiation without the constraints of flat tissue culture vessels, allowing for autonomous self-organization of cells. Such models allow the formation of miniature organs in a dish and are emerging for the pancreas, starting from embryonic progenitors and adult cells. This review focuses on the currently available systems and how these allow new types of questions to be addressed. We discuss the expected advancements including their potential to study human pancreas development and function as well as to develop diabetes models and therapeutic cells.