With respect to the future urban mobility, modern electrical bicycles, advanced motorcycles and innovative two-wheeled vehicles are arresting enormous amount of attention. Especially, model-based control and optimal trajectory planning for such vehicles are important to the research and development of the future. Therefore, a reliable and yet usable vehicle model as well as a systematic approach to motion control for two-wheeled vehicles are essential, to which this work makes a contribution. Currently available two-wheeled vehicle models are mostly either too complex to be used for a systematic control synthesis, or too simple such that the physical behaviour of the vehicle is no more represented. In this thesis, a unifying approach to modelling and control for autonomous two-wheeled vehicles is presented. The resulting model is generally valid and physically detailed enough to represent the characteristic dynamical behaviour such as the self-stability. At the same time, it is suited to a systematic control synthesis. Furthermore, the systematic extenddability, for instance by a rider, is demonstrated. The model is validated by simulations and by comparison to well-known models from the literature. The proposed vehicle model is derived in the Lagrangian and Hamiltonian framework and used for model-based optimal trajectory planning. Furthermore, a passivity-based trajectory tracking controller is designed based on the resulting port-Hamiltonian system using the so-called generalised canonical transformations. Such a controller is physically interpretable and robust against parameter uncertainties. To this end, existing approaches of passivity-based controller design are extended and adjusted for two-wheeled vehicles. Finally, a prototype two-wheeled vehicle is introduced which is used for experimental validation of the model and to demonstrate motion control algorithms for autonomous two-wheeled vehicles.