Abstract:Pharmaceutical Quality by Design (QbD) emphasizes comprehensive understandings of multidimensional combinations and interactions among raw materials, process and product quality during the pharmaceutical manufacturing processes. Such understandings could be realized by mathematical models, which characterize the “input-output” relationships of process systems and are important tools for explaining the laws of pharmaceutical quality transfer and predicting final product critical quality attributes (CQAs). Based on the quality risk management principles and the influence of mathematical models on the final product quality, process models were divided into high, medium and low risk categories. And good modeling practice (GMoP) was introduced to standardize the modeling process and to improve the efficiency of process modeling. This paper also summarized the methods of mechanistic model, statistical model and hybrid model, and reviews the applications of mathematical models to the extraction, drying, granulation, powder compression, process monitoring and control, and application of process system characterization.