Compartmentalization of biological content and function is a key architectural feature in biology, where membrane bound micro- and nanocompartments are used for performing a host of highly specialized and tightly regulated biological functions. The benefit of compartmentalization as a design principle is behind its ubiquity in cells and has led to it being a central engineering theme in construction of artificial cell-like systems. In this review, we discuss the attractions of designing compartmentalized membrane-bound constructs and review a range of biomimetic membrane architectures that span length scales, focusing on lipid-based structures but also addressing polymer-based and hybrid approaches. These include nested vesicles, multicompartment vesicles, large-scale vesicle networks, as well as droplet interface bilayers, and double-emulsion multiphase systems (multisomes). We outline key examples of how such structures have been functionalized with biological and synthetic machinery, for example, to manufacture and deliver drugs and metabolic compounds, to replicate intracellular signaling cascades, and to demonstrate collective behaviors as minimal tissue constructs. Particular emphasis is placed on the applications of these architectures and the state-of-the-art microfluidic engineering required to fabricate, functionalize, and precisely assemble them. Finally, we outline the future directions of these technologies and highlight how they could be applied to engineer the next generation of cell models, therapeutic agents, and microreactors, together with the diverse applications in the emerging field of bottom-up synthetic biology.