This book deals with damping problems in bridges and focuses on the mechanisms and the factors affecting the dynamic behavior of bridges with damping devices. It presents the state-of-the-art of engineering practice in bridge dynamics. After a short historical introduction given in the first chapter, some basic introductory concepts related to the necessary mathematical background are presented in the second chapter. In the third chapter, the basic dynamic loadings such as wind and earthquake according to current codes are presented. In the fourth chapter, the most commonly applied dynamic models of bridges with internal and external damping systems are presented in detail. In chapter five, one can see nine representative examples that are presented in full detail. In this last chapter, applications regarding rocking, overturning and shifting problems in bridges, damping systems in external cables, bridges resting on elastomeric bearings, bridges with internal damping systems, friction and rolling pendulum bearings, and cables with movable anchorages are given in the form of illustrative examples with analytical and numerical solutions.