The bottom-up assembly of biological and chemical components opens exciting opportunities to engineer artificial vesicular systems for applications with previously unmet requirements. The modular combination of scaffolds and functional building blocks enables the engineering of complex systems with biomimetic or new-to-nature functionalities. Inspired by the compartmentalized organization of cells and organelles, lipid or polymer vesicles are widely used as model membrane systems to investigate the translocation of solutes and the transduction of signals by membrane proteins. The bottom-up assembly and functionalization of such artificial compartments enables full control over their composition and can thus provide specifically optimized environments for synthetic biological processes. This review aims to inspire future endeavors by providing a diverse toolbox of molecular modules, engineering methodologies, and different approaches to assemble artificial vesicular systems. Important technical and practical aspects are addressed and selected applications are presented, highlighting particular achievements and limitations of the bottom-up approach. Complementing the cutting-edge technological achievements, fundamental aspects are also discussed to cater to the inherently diverse background of the target audience, which results from the interdisciplinary nature of synthetic biology. The engineering of proteins as functional modules and the use of lipids and block copolymers as scaffold modules for the assembly of functionalized vesicular systems are explored in detail. Particular emphasis is placed on ensuring the controlled assembly of these components into increasingly complex vesicular systems. Finally, all descriptions are presented in the greater context of engineering valuable synthetic biological systems for applications in biocatalysis, biosensing, bioremediation, or targeted drug delivery.