  Eukaryotic cells and intracellular pathogens such as bacteria or viruses
utilize the actin polymerization machinery to propel themselves forward.
Thereby, the onset of motion and choice of direction may be the result of a
spontaneous symmetry-breaking or might be triggered by external signals and
preexisting asymmetries, e.g. through a previous septation in bacteria.
Although very complex, a key feature of cellular motility is the ability of
actin to form dense polymeric networks, whose microstructure is tightly
regulated by the cell. These polar actin networks produce the forces necessary
for propulsion but may also be at the origin of a spontaneous
symmetry-breaking. Understanding the exact role of actin dynamics in cell
motility requires multiscale approaches which capture at the same time the
polymer network structure and dynamics on the scale of a few nanometers and the
macroscopic distribution of elastic stresses on the scale of the whole cell. In
this chapter we review a selection of theories on how mechanical material
properties and growth processes interact to induce the onset of actin based
motion.
