This article examines the ‘active’ part of the cell cytoskeleton — which mostly corresponds to actin and tubulin polymers and associated molecular motors — using theoretical tools derived from a soft matter physics coarse-grained approach. It begins with an overview of the cytoskeleton and its components, which include actin filaments and gels, microtubules and specialized microtubule-based organelles, molecular motors, intermediate filaments, the plasma membrane and glycocalix, the cell wall, and the extracellular matrix. It then describes coarse-grained models of the cytoskeleton and gives two examples of models for important cellular functions, namely cell migration and cell polarity. It also proposes a new kind of soft matter model providing a coarse-grained description of cytoskeletal polymers and associated molecular motors.