In recent years, significant advances have been made towards compensating respiratory organ motion for the treatment of tumours, e.g. for the liver. Among the most promising approaches are statistical population models of organ motion. In this paper we give an overview on our work in the field.We explain how 4D motion data can be acquired, how these motion models can then be built and applied in realistic scenarios. The application of the motion models is first shown on a case where 3D surrogate marker data is available. Then we will evaluate the prediction accuracy if only 2D and lastly 1D surrogate marker motion data is available. For all three scenarios we will give quantitative prediction accuracy results.