The dynamic interaction between the bridge and the passing vehicle or train is considered a point of interest concerning the railway bridge design and maintenance, and the interest becomes greater for the bridges serving as links on high-speed lines. In this paper, the interaction problem is presented through the different models used to describe the phenomenon and the different techniques adopted to solve the non-linear interaction problem. The models describing the problem vary greatly from very simple 2D models with moving loads over beams to complex 3D models with multiple degrees of freedom (DOFs) for both the bridge and vehicle and with precise definition of various parts and parameters affecting the response such as the type of bridge element, the track structure and the bridge elastic supports. The solution algorithms of the non-linear interaction problem also vary from simple analytic solutions and non-direct techniques to more sophisticated iterative techniques in finite element (FE) domains.