Morphogenetic patterns at the level of cells and tissues arise from a tight coupling between signaling, mechanics and dynamical geometry. The actomyosin cytoskeleton is a prime orchestrator of this coupling. We will discuss minimalistic theoretical models for the emergence of mechanochemical patterns in such active materials. We will then show that a simple linear turnover reaction for the active stress regulator (myosin) leads to the emergence of nonlinear traveling waves in these models. Considering such active patterns on curved surfaces, we will demonstrate the emergence of non-trivial curvature induced waves in a polar flock confined to a curved surface. Finally, we will develop a framework to study these nonequilibrium patterns on dynamical geometries wherein the mechanical forces needed for shape deformation are controlled by active mechanochemical stresses. As an example of this geometrodynamics of active materials, we will present preliminary results that lead to spontaneous asymmetries during the ingression of the cytokinetic furrow.