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Particulate filters (PF) are a highly effective after-treatment device that reduces particulate matter emissions, a rising environmental concern in the automotive industry. However, accumulation of solid particles during the PF filtration process increases engine backpressure considerably, which can have a negative impact on engine efficiency, acoustics, and gaseous emissions. In this area, an accurate pressure drop model helps to better understand the effect of accumulated solid particles in the PF on engine backpressure, aiding in design and regeneration considerations without physical testing. These effects are further improved on board the vehicle using a single equation pressure drop model with a relatively low computational cost. This article presents a thorough history of PF pressure drop models and their advancements.