With the recent dawn of synthetic biology, the old idea of man-made artificial life has gained renewed interest. In the context of a bottom-up approach, this entails the de novo construction of synthetic cells that can autonomously sustain themselves and proliferate. Reproduction of a synthetic cell involves the synthesis of its inner content, replication of its information module, and growth and division of its shell. Theoretical and experimental analysis of natural cells shows that, whereas the core synthesis machinery of the information module is highly conserved, a wide range of solutions have been realized in order to accomplish division. It is therefore to be expected that there are multiple ways to engineer division of synthetic cells. Here we survey the field and review potential routes that can be explored to accomplish the division of bottom-up designed synthetic cells. We cover a range of complexities from simple abiotic mechanisms involving splitting of lipid-membrane-encapsulated vesicles due to physical or chemical principles, to potential division mechanisms of synthetic cells that are based on prokaryotic division machineries.