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The evolution of computer resources paved the way for numerical models to substitute extensive experimental campaigns to develop and optimize compressors for the HVAC&R industry. A particular class of compressor models referred to as mechanistic (or deterministic) chamber model is well-known to be computationally efficient and has reasonable model fidelity for performance prediction and extrapolation. The overall model architecture requires inputs from various sub-models, including the mass flow, heat transfer and valve models. The accuracy of the overall model depends on the fidelity and accuracy of the individual sub-models. This article provides a comprehensive review of the different approaches available in literature which were used to model the geometry, mass flow, valves, and heat transfer processes in the compressor. The article aims to help researchers identify suitable approaches for their analysis. Additionally, it was found that there are opportunities for additional research to develop analytical correlations for discharge coefficients for the mass flow model, explore solubility in leakage gaps, develop effective flow/force area estimation for valve models, and develop instantaneous heat transfer coefficients for specific compressor architectures and thermal conductance models for multi-lumped network models. [ABSTRACT FROM AUTHOR]