In the last five decades, continuum damage mechanics has proven to be a valuable tool to study material degradation. Many damage models have been developed that allow an accurate description of damage processes for a wide range of materials. At the same time, much effort has been expended to develop robust algorithms for obtaining numerical solutions to problems with damage. Some of the models have already been implemented in commercial finite element codes and have become a valuable tool in helping engineers predict behavior of engineering structures. In this article, a general framework for modeling damage, based on the theory of irreversible thermodynamics with internal variables, is outlined. Special attention is devoted to issues related to the numerical implementation of material models with damage, such as mesh sensitivity of the solution and convergence difficulties.