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Fibrous filters are commonly utilized to remove aerosols from the air to capture contaminants and pollutants prior to atmospheric release, or to clean atmospheric air itself. An ideal filter achieves the highest capture efficiency possible while providing the least airflow resistance possible. From this, the ability to predict how a filter operates based upon its functional parameters, such as filtration velocity and particle size and type, and characteristic parameters, such as its fiber size and media porosity, are integral to not only properly applying and estimating filter performance, but also facilitating the improvement and development of filtration technology. The purpose of this work is to review both classical and contemporary particle loading models to provide a comprehensive discussion built upon a foundation of first principles. The different relevant particle capture mechanisms are presented and discussed in terms of fibrous air filtration, along with the separate loading regimes. Specific loading models are then introduced considering these concepts and are separated into three categories: 1) analytical models, 2) computational models, and 3) experimental models. In short summary, analytical models have been well-covered and benefit from their ease of use but suffer from a difficulty in describing the stochastic nature of realistic particle loading. Computational models benefit from their inherent incorporation of first principles thereby addressing the dynamic nature of particle loading, however they may be difficult to apply outside of research environments due to their complexity and computationally demanding nature. Experimental models benefit from the avoidance of simplifying assumptions and the ability to correlate data describing phenomena that are difficult to quantify but are limited to applications covered by their experimental parameters and have difficulty addressing anomalies that present themselves. Suggested future work from identified research gaps focus on the lack of available data and reliable methods to measure media characteristics as well as developing models that predict the full spectrum of the loading process based upon media and particle characteristics. • Particle loading models predict filter performance from factors such as loaded mass. • Prevalent work is categorized as analytical, computational, or experimental. • Included models are presented in terms of foundational particle capture mechanisms. • Strengths and weaknesses of the model categories are presented and discussed. • Future work is identified through current research gaps. [ABSTRACT FROM AUTHOR]