This review article is intended to serve as an overview of the current status of the computational tools and approaches available for predicting respiratory-tract dosimetry of inhaled particulate matter. There are two groups of computational models available, depending on the intended use. The whole-lung models are designed to provide deposition prediction for the whole lung, from the oronasal cavities to the pulmonary region. The whole-lung models are generally semi-empirical and hence provide more reliable results but within the range of parameters used for empirical correlations. The local deposition or computational fluid dynamics (CFD)-based models, on the other hand, utilize comprehensive theoretical and computational approaches but are often limited to upper respiratory tracts. They are based on theoretical principles and are applicable to a wider range of parameters, but less accurate. One of the difficulties with modeling of aerosol deposition in human lung is related to the complexity of the airways geometry and the limited morphometric data available. Another difficulty corresponds to simulation of the realistic physiological conditions of lung environment. Furthermore, complex physical and chemical phenomena associated with dense and multicomponent aerosols complicate the modeling tasks. All of these issues are addressed in this review. The progress made in each area in the last three decades and the challenges ahead are discussed along with some suggestions for future direction. The following subjects are covered in this review: introduction, aerosol deposition mechanisms, elements of a computational model, respiratory-tract geometry models, whole-lung models, CFD based models, cigarette smoke deposition models, and conclusion.