We study the space–time dynamical behavior of broad-area semiconductor lasers, using an extended phenomenological laser model to include transverse diffraction of the counterpropagating optical fields and transverse diffusion of carriers. Numerical results show that the profile of the output intensity exhibits spatiotemporal chaos by way of changing random filaments. A small confinement factor and/or linewidth enhancement factor can prevent instabilities. Simulations also confirm experimental results showing that a half-symmetric unstable resonator with a suitable mirror curvature restores stability.