How do the cells in our body reconfigure their shape to achieve complex tasks like migration and mitosis, yet maintain their shape in response to the forces exerted by for instance blood flow and muscle action? Cell shape control is defined by a delicate mechanical balance between active force generation and passive material properties of the plasma membrane and the cytoskeleton. The cytoskeleton forms a space-spanning fibrous network comprising three subsystems; actin, microtubules and intermediate filaments. Bottom up reconstitution of minimal synthetic cells where these cytoskeletal subsystems are encapsulated inside a lipid vesicle provides a powerful avenue to dissect the force balance that governs cell shape control. Although technically demanding, a steady stream of advances in encapsulation techniques has made the reconstitution of shape-changing minimal cells increasingly feasible. In this topical review we provide a route-map of the recent advances in cytoskeletal encapsulation techniques and outline recent reports that have demonstrated shape change phenomena in simple biomimetic vesicle systems. We end with an outlook towards the next steps required to achieve more complex shape changes with the ultimate aim of building a fully functional synthetic cell with the capability to autonomously grow, divide and move.