Continuum damage mechanics elaborates the continuum mechanics-based modelling and simulation of mechanical degradation effects. The objective of this contribution is to briefly review different aspects of continuum damage mechanics of solid continua with a focus on general modelling concepts and application to isotropic as well as anisotropic damage approaches on the one hand, and to discuss possible solution strategies in the context of finite element simulations on the other. In particular, viscous regularisation and gradient-enhanced regularisation—as a reduced form of general non-local theories—are considered. Several numerical examples including ductile damage, i.e. the coupling of damage with plasticity related phenomena, are addressed which show the applicability of the particular modelling and simulation frameworks highlighted.