The rail vehicle suspension is the set of elastic elements, dampers and associated components that connect the wheelsets to the car body, often via bogie frames. Even linkages such as traction rods are often regarded as suspension elements. Suspension elements are designed to have certain force-displacement characteristics, or force-velocity characteristics in the case of dampers, to guarantee running safety and to provide good ride characteristics to the vehicle. In this chapter, the various suspension elements used in rail vehicles, namely coil springs, rubber springs, air springs, leaf springs and hydraulic dampers are introduced and their main characteristics explained. Proposals on how to model them for vehicle dynamics simulations and guidance for further reading are given. Also, constraints and bumpstops, i.e., devices that limit relative displacements, are described. In the final sections, a number of different carbody-to-bogie connections are introduced.