Stress fibres are contractile acto-myosin structures found from many types of non-muscle cells, where they are involved in adhesion, motility and morphogenesis. Stress fibres typically display a periodic alpha-actinin-myosin II pattern and are thus suggested to resemble the sarcomeric actin filament structures of muscle cells. Mammalian cells contain three categories of stress fibres: ventral stress fibres that are attached to focal adhesions at both ends, dorsal stress fibres that are attached to focal adhesions typically at one end and transverse arcs that are curved acto-myosin bundles, which do not directly attach to focal adhesions. In this review, we discuss the definition of stress fibres, organization of actin filaments and other components within these contractile structures, and the mechanisms of stress fibre assembly.