In this report, a complete review of the modeling and control schemes employed for overhead cranes has been provided. Different kinds of modeling strategies used for numerical simulations and controllers have been reviewed and their properties and validity have been discussed. Subsequently, the control methods introduced for overhead cranes are reviewed and their characteristics and stability have been analyzed. The studied modeling and control methods are then classified in tabular formats allowing one to select the most appropriate strategy for each specific application at a glance. Finally, some controllers have been selected from each class of controllers and comparative numerical experiments have been made to extract the key characteristics of each method. In the end, some comments and recommendations are provided to select the best modeling and control methods for each specific application