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High energy laser propagation in an absorbing medium is described by the Fresnel equation with a nonlinear term.While perturbative solutions exist for some special simple cases, the most useful approach has required development of efficient computer algorithms to satisfactorily solve problems of interest. This paper reviews the numerical techniques which iteratively solve nonlinear laser propagation problems and indicates the agreement obtained in comparison with laboratory experiments. The wide range of physical effects in addition to the nonlinear phenomena which are also included in the computer codes to predict the propagation of the laser beam from the laser cavity, through the optical train and into the atmosphere are also discussed. AbstractHigh energy laser propagation in an absorbing medium is described by the Fresnel equation with a nonlinear term. While perturbative solutions exist for some special simple cases, the most useful approach has required development of efficient computer algorithms to satisfactorily solve problems of interest. This paper reviews the numerical techniques which iteratively solve nonlinear laser propagation problems and indicates the agreement obtained in comparison with laboratory experiments. The wide range of physical effects in addition to the nonlinear phenomena which are also included in the computer codes to predict the propagation of the laser beam from the laser cavity, through the optical train and into the atmosphere are also discussed.