Actin polymerization generates the force that deforms the cell membrane, pulls the cell forward and propels endosomes and bacteria within the cell. The mechanism of force generation has been probed using experimental biomimetic systems where force generation and movement occur by the same actin-polymerization processes observed in cells. The advantage of such systems over living cells is that their physical properties can be changed, such as the size of the load, its composition and its deformability, in order to respond to specific questions. Recent experimental developments and associated theoretical models have provided us with a better understanding of motility based on actin polymerization. This paves the way towards a better comprehension of cell motility.