The construction of an irreducible minimal cell having all essential attributes of a living system is one of the biggest challenges facing synthetic biology. One ubiquitous task accomplished by any living systems is the division of the cell envelope. Hence, the assembly of an elementary, albeit sufficient, molecular machinery that supports compartment division, is a crucial step towards the realization of self-reproducing artificial cells. Looking backward to the molecular nature of possible ancestral, supposedly more rudimentary, cell division systems may help to identify a minimal divisome. In light of a possible evolutionary pathway of division mechanisms from simple lipid vesicles toward modern life, we define two approaches for recapitulating division in primitive cells: the membrane deforming protein route and the lipid biosynthesis route. Having identified possible proteins and working mechanisms participating in membrane shape alteration, we then discuss how they could be integrated into the construction framework of a programmable minimal cell relying on gene expression inside liposomes. The protein synthesis using recombinant elements (PURE) system, a reconstituted minimal gene expression system, is conceivably the most versatile synthesis platform. As a first step towards the de novo synthesis of a divisome, we showed that the N-BAR domain protein produced from its gene could assemble onto the outer surface of liposomes and sculpt the membrane into tubular structures. We finally discuss the remaining challenges for building up a self-reproducing minimal cell, in particular the coupling of the division machinery with volume expansion and genome replication.