Scour, defined by the loss of geomaterials surrounding a foundation support system, is a primary cause of bridge failure in the United States and worldwide. Work herein presents a comprehensive review of the current state of knowledge on geotechnical aspects of erodibility, factors influencing pier scour, factors complicating pier scour assessment, and databases available on erodibility and pier scour. A summary of deterministic pier scour models, developed since 1990, is presented in view of the factors affecting scour rate and equilibrium magnitude. The study discusses challenges in the predictive approaches reviewed in the paper. In addition, advancements in probabilistic pier scour models, and observation-based models are summarized. Four pier scour models, namely Wilson (1995) model, Melville (1997) model, Hydraulic Engineering Circular No. 18 (2012) model, and Briaud (2014) model are comparatively applied to data from laboratory pier scour database. Error statistics and accuracy, precision, and probabilistic distribution of predictions from these models are presented and discussed.