This thesis investigates passively mode-locked semiconductor lasers by numerical methods. The understanding and optimization of such devices is crucial to the advancement of technologies such as optical data communication and dual comb spectroscopy. The focus of the thesis is therefore on the development of efficient numerical models, which are able both to perform larger parameter studies and to provide quantitative predictions. Along with that, visualization and evaluation techniques for the rich spatio-temporal laser dynamics are developed; these facilitate the physical interpretation of...