This paper presents ideas of random set modeling of fire spread, corresponding algorithms of model parameter estimation, and prediction of fire spread. Some facts indicating the stochastic nature of fire spread are reviewed. A brief survey of deterministic and stochastic models of spread and a description of random set models based on a Markov process called random spread process (RSP) is given. Random set models of local fire spread are considered in more detail. Results of a theory of estimation of RSP model parameters are used. Experimental and real fire data obtained by some Russian research institutes and fire protection services are discussed. This paper shows how random set models of fire spread may be used in computer experiments of fire modeling. Also, a comparison between real and computer data is established. A summary is given of the software for protecting territory from fire, based on random set models of fire spread. Applications of the software for the simulation of forest and timber-yard fire spread under given weather conditions are presented. Supporting theories of set-means and of random set models of spread and computational aspects are in the Appendix. Finally, a few references to the vast Russian literature on modeling of fire spread are given.