Vesicles are membrane compartments in aqueous solutions consisting of self-assembled amphiphilic molecules such as lipids. Before the first living systems emerged from non-living forms of matter, functional macromolecules and vesicles must have assembled to form prebiotic self-reproducing compartment systems called “protocells.” Although we cannot observe protocells today, recent advances in soft matter physics, systems chemistry, and synthetic biology are making steady progress in our bottom-up understanding of what bridges non-living and living systems. In this review, we focus on the vesicular compartment aspect of recent protocell research and provide a membrane physics background that helps us understand how protocells reproduced themselves four billion years ago. In addition to prebiotically plausible reactions and dynamics, we also focus on the non-natural (or artificial) approaches that can achieve the same essential concepts of protocells in different ways from biological systems. Therefore, this review will provide knowledge on vesicles also for researchers and students interested in artificial cells and minimal cells.