Organoids are multicellular structures that can be derived from adult organs or pluripotent stem cells. Early versions of organoids range from simple epithelial structures to complex, disorganized tissues with large cellular diversity. The current challenge is to engineer cellular complexity into organoids in a controlled manner that results in organized assembly and acquisition of tissue function. These efforts have relied on studies of organ assembly during embryonic development and have resulted in the development of organoids with multilayer tissue complexity and higher-order functions. We discuss how the next generation of organoids can be designed by means of an engineering-based narrative design to control patterning, assembly, morphogenesis, growth, and function.