The evolution of solid-state laser systems over the past decade, both through technological advances and through increased understanding of the interplay between nonlinw effects and linear diffraction, is reviewed. The role of numerical methods to simulate the several physical processes (diffraction, self-focusing, gain saturation) involved in coherent beam propagation through large laser systems is discussed. A comprehensive simulation code for modeling all of the pertinent physical phenomena observed in laser operations (growth of small-scale modulation, spatial filtering, imaging, gain saturation, and beam-induced damage) is described in detail. The realism and accuracy of results obtained with this numerical code stem from an unambiguous identification of the sources of spatial noise, and from the use of spatial filters in modern lasers to limit the transverse beam modulation scale within the practical computational range of a two-dimensional numerical analysis. Several comparisons between code results and solid-state laser output performance data are presented. Finally, the design and performance estimation of the large Nova laser system presently under construction at the Lawrence Livermore National Laboratory (LLNL) are given. M