Thermomechanical modeling of laser material processing in general, and defect modeling in particular, has raised attention in both academia and industry for the last twenty years. Additive manufacturing (aka, 3D printing) is increasingly studied and utilized by researchers and engineers. Defects created during a part building process are costly to identify and could cause premature part failure, and thus numerous studies and research projects have been conducted in order to predict and analyze defects in laser material processing. The available information for defect modeling is scattered widely in the literature and mostly dedicated to very small and specific areas of focus, making it difficult for others to follow, even though the quantity of information is not small. In this work, a review of defect modeling which focuses specifically on the defect types existing in additive manufacturing industry has been carried out, including over 140 referenced articles.