Abstract An overview of the state of the art of computational fracture mechanics is presented, starting from early efforts and going all the way up to recent achievements. Some specific aspects of linear elastic and elastic plastic fracture mechanics problems have been discussed, including the fact that even for a static loading, numerical simulation is not a simple task because of complex geometries, material nonlinearity, and heterogeneity, and especially if crack growth is considered. Therefore, micromechanical modelling of elastic‐plastic crack growth is presented as new and promising approach to overcome some of the shortages of traditional approach. Besides static loading, couple of other important practical problems are tackled, like fatigue crack growth, with remaining life in the focus of investigation, using the empirical laws for crack growth rates. Numerical simulation of fatigue crack growth is inherently complex both because of complex material damage processes and lack of sound theoretical basis to define them. Therefore, combination of theoretical, experimental, and numerical approach is presented here to get reliable and efficient estimation of life under fatigue loading.