Rutting is one of the significant distresses in flexible pavements. Examining the methods to decrease permanent deformation is of considerable importance to provide long service life and safe highways. The main objective of this paper is to undertake a state-of-the-art review to combine the existing work on the permanent deformation of asphalt concrete pavements. For this purpose, the review synthesizes the evolution of the permanent deformation models, the tests methods used to evaluate and quantify the rutting potential of asphalt mixtures with a particular focus provided on the stress sweep rutting test which is gaining popularity as it tackles the shortcomings of its predecessor for the exact characterization and prediction of permanent deformation. Additionally, some advanced computational intelligence methodologies such as finite element model and soft computing are reviewed. Furthermore, the most common permanent deformation solutions are reviewed. It was found that efforts are put towards improving either the rheological properties of base asphalt by using modifiers or asphalt mixture by using selected aggregates to enhance the aggregate interlock and by implementing semi-flexible asphalt pavements which is expected to be a promising method against permanent deformation. This state-of-the-art work is expected to supply a comprehensive perception of the available models, rutting test, and solutions, and to suggest future studying areas related to the rutting of asphalt pavements.