The paper deals with the investigation of some phenomena which are essential for dynamic interaction of a wheelset or bogie with the railways track. The track is modeled as discrete-continuous system composed of rails, fastening systems and sleepers interacting with ballast by means of viscous-elastic elements. Transient and stationary problems are investigated. The stationary periodic problems are connected with wave propagation in stopping bound, passing bound and mistuning. In this paper, a review of selected problems and exemplary results of simulation and experimental investigations is given supplemented by a few results of analysis and simulation.