The wheel-rail interface is a complex component of the dynamic railway vehicle-track system. The wheel-rail interface governs the motion of a railway vehicle and is responsible for wheel and track damage such as wear and rolling contact fatigue. Wheelrail contact models are used extensively in railway engineering to calculate contact forces and stresses, in order to evaluate dynamic vehicle behaviour or assess track damage. Due to the complexity of the wheel-rail interaction, and computational limitations, all wheel-rail contact models make simplifying assumptions so that solutions may be obtained in an acceptable time. This thesis presents a survey of current wheel-rail contact models and theories, and associated literature, focussing on the various simplifications made by the different approaches. In order to allow an informative comparison of contact model performance a wheel-rail contact benchmark has been established, detailing carefully defined, challenging contact conditions. Interested parties were invited to submit solutions for the contact benchmark cases, and results from ten contributors were received and compared. From the analysis of current contact models and the contact benchmark results, a new wheel-rail contact model has been developed. The model is based on a novel relationship between the normal contact force and the intersecting volume found from virtually penetrating two, three dimensional contacting bodies. Results from the new contact model, named the 'Rectified Interpenetration method', were compared favourably to the recognised methods of Hertz and Kalker. To aid future validation of wheel-rail contact model and understanding of the wheel. rail interaction, a feasibility study of a new wheel-rail contact measurement technique has been undertaken. The technique is based on an established ultrasound method capable of measuring the normal contact pressure distribution for machined wheel and rail samples in laboratory conditions. The new technique aims to advance the state of the art to allow wheel-rail contact measurements under rolling conditions. The study concluded that there is scope for further development of the technique, and discusses the transitional difficulties in advancing the static method to rolling contacts.