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The latter two decades of the last century saw significant improvements in External Beam Radiotherapy (EBRT), moved primarily by the advances in imaging modalities and computer-based treatment planning. These advances led to introducing the addition of a fourth dimension, time, to the three-dimensional EBRT arena. This new era in EBRT brings with it challenges and opportunities, in particular to compensate for the effect of respiratory-induced target motion and enhancing treatment delivery. Thus, characterising and modelling respiratory motion is of major importance in this research area. This thesis aims to enhance the understanding and control the effect of respiratory motion. As part of this work, the first principal component analysis (PCA) of respiratory motion is presented, as a basis for compactly and visually representing respiratory style and variation. These studies can be divided into two main aspects: firstly, understanding and characterising respiratory motion as the basis of any further steps towards compensating respiratory motion and secondly, utilising this knowledge in predicting and correlating internal and external respiratory motion in the abdominal thoracic region. This work has been developed starting with a piecewise sinusoidal model in an Eigenspace for modelling. Adaptive kernel density estimation (AKDE) for prediction and finally Canonical Correlation Analysis (CCA) for external-internal target correlation. A comparative study between these proposed approaches and state-of-the-art prior works showed promising results in terms of accuracy and computational efficiency: 20% error reduction compared to support vector regression (SVR) and kernel density estimation (KDE) and a significant reduction in computation speed during training stage. This journey into modelling and predicting respiratory behaviour has naturally raised questions of how best to track external motion. The need to track the surface with more than one marker, established within the aforementioned PCA analysis, motivates the desire for markerless tracking. Therefore, two different markerless systems have been studied, as potential solutions for this area, combined with a mesh model of the anterior surface. This suggests that the Microsoft Kinect camera is a promising low-cost technology for makerless respiratory tracking with less than 3. 1 +- 0. 6 mm accuracy.