The collective motion of driven or self-propelled interacting units is in many natural systems
known to produce complex patterns. This thesis considers two continuum field theories commonly
used in describing pattern formation and dynamics: The first one, the phase field crystal
model, which describes the dynamical and equilibrium properties of crystalline material,
is used to study the coarsening dynamics of polycrystalline materials in two and three dimensions.
A generalization introducing a faster elastic relaxation time scale is then used to study
the plastic deformation and dislocation dynamics of single crystals. Secondly, a continuum
theory describing mesoscopic turbulence of biological active matter, which is used to study
long-range ordered vorticity patterns generated by cell divisions in a endothelial cell layer.