This study focuses on problems devoted to application of ballastless track on railway bridges. The different kind of this track are presented and its advantages and faults. A special attention is given to generated vibration and noise by moving trains and their influence on behaviour of bridge structure. Methods of dumping are presented too. Transfer of longitudinal forces in lateral and longitudinal direction is given. Interaction between continuous welded rail and bridge structure is written. Longitudinal resistance of fastening system for ballastless track is also given. Using of sealing layer between track and bridge deck is considered. Problems relating to uplift od of the girder ends are given. Cracks in concrete elements of ballastless track on the bridge structure is considered. Some of the solutions of mentioned above problems are given in general design rules produced by different organizations and some are or will be given in current or prepared standards.