Living matter is highly dynamic and organizes in complex patterns and spatial structures. A fundamental question in biology is to understand how cells break symmetries. Examples for cell symmetry breaking are cell polarity and cell chirality, which play an important role during the formation of complex organisms. Cell symmetry breaking is often mediated by active dynamical processes. The prototype of such active processes is force generation by motor molecules. Molecular motors are driven by the chemical energy of a fuel. They generate movements and forces on molecular scales. Active force generation gives rise to unconventional mechanical behaviors and spontaneous movements of the gel-like materials inside the cell. I will discuss the basic physics of active cellular processes and the mechanisms by which cellular flow patterns are generated. I will show that such flows provide a key mechanism for cellular symmetry breaking that can guide the establishment of the main body axes as well as the left-right asymmetry of developing organisms.