Recent applications of the breathing sphere model for molecular dynamics simulations of laser ablation of organic solids have yielded detailed microscopic data of the processes involved. The results to date include a prediction of a fluence threshold for ablation, an explanation for the presence of clusters in the plume and a consistent analytical description of the velocity distribution for both matrix molecules and heavier analyte molecules in matrix-assisted laser desorption. In this paper we review the approach and the basic physical picture that emerges from the simulations, present new results, and discuss future prospects for microscopic simulations of laser ablation.