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Laser beam machining (LBM) is a widely used thermal advance machining process capable of high accuracy machining of almost any material with complex geometries. CO₂ and Nd:YAG lasers are mostly used for industrial purposes. Drilling, cutting, grooving, turning and milling are the applications of LBM with different material removal mechanisms. Modeling and simulation of the LBM process is indispensable for optimization purposes. Modeling can be done by implementing analytical, numerical, experimental and artificial intelligence-based methods. This paper provides a review of the various methods used for modeling and simulation of the laser beam machining process as well as key researches done in this field so far.