In this paper, studies on dynamic modeling, simulation and experiment of power transmission belt drives are comprehensively reviewed. In the past few decades, many investigations are conducted on dynamic modeling, simulation and experiment of different kinds of power transmission belt drive systems. In the dynamic modeling and simulation of the belt drive systems, surveys are focused on vibrations of a single axially moving belt span, rotational vibrations of pulley components, coupled belt-pulley vibrations and contact mechanics between the belt and pulley as well as some experimental investigations. Influences of tensioner dry friction and one-way clutch on dynamics of the belt drive systems including system rotational vibrations and coupled belt-pulley vibrations are separately reported. The investigations are also surveyed on modeling and predicting complicated belt-pulley contact behaviors like belt creeps and slips on pulleys, contact force distributions of the belt and pulley, and variation of wrap angles of a belt around pulleys, etc., which are categorized by different approaches including the creep theory, shear theory, multi-body dynamics and finite element methods. Fatigue life estimation and failure analysis of power transmission belt drives are discussed in detail as well. In addition, experimental techniques are reviewed on parameters identifications, and measurements of static and dynamic performances including energy/power loss, system vibration, dynamic belt tension, belt deformation, stress and strain distribution in the belt and pulley, and contact friction force, etc. Finally, conclusion of this work is summarized and topics of future potential studies on the power transmission belt drive systems are suggested.