The blood flow patterns in vivo are highly complex; they vary considerably from subject to subject and even more so in patients with cardiovascular diseases. Over the last five years, there has been a rapid surge of interest in combining computational fluid dynamics (CFD) with in vivo imaging techniques for studying interactions between vessel morphology and blood flow patterns. CFD gives the ability to compute features/properties which cannot be measured, e.g. wall shear stress, mass transfer rate, but are important to studies of atherosclerosis, or the design of vessel prostheses. Moreover, it can also provide details of the flow which are often beyond the discrimination of the imaging techniques. This trend is driven by our increased understanding of biomechanics, maturity of computational modelling techniques, and advancement in imaging. To this end, accurate delineation of cardiac morphology and its associated in-flow/out-flow tracts is required. Due to the complex topology of the dynamic shapes involved, this procedure usually involves labour-intensive user interaction with a large amount of 4D spatio-temporal information. With the increasing popularity of the active shape and appearance models, 3D shape modelling and segmentation based on these techniques are gaining significant clinical interest. The practical quality of the statistical model relies on the definition of correspondence across a set of segmented samples. For time-varying 3D cardiovascular structures, landmarks based techniques are not only time consuming but also prone to subjective error, as temporal alignment of geometrical features is difficult. Moreover, when all of the structures including inflow/outflow tracts are considered, the shape to be modelled becomes highly complex even in its static form. This makes the identification of dense correspondence within the training set a significant challenge. The purpose of this thesis is to develop a practical approach towards optimal statistical modelling and segmentation for dynamic 3D objects with complex topology. The method relies on harmonic embedding for establishing optimal global correspondence for a set of dynamic surfaces. We first demonstrate how it can be used for shapes whose topological realization is homeomorphic to a compact 2D manifold with boundary. A conformal harmonic map and tensor product B-splines are used to create a multi-resolution representation of the surfaces that are re- parameterized by using hierarchical piecewise bilinear maps in a coarse-to-fine manner. The optimal global correspondence within the training shapes is identified by an objective function based on the principle of minimum description length. The strength of the method is demonstrated by building a concise yet physiologically plausible statistical shape model of the normal human left ventricle which has principal modes of variation that correspond to intrinsic cardiac motions. The proposed framework is then extended to dynamic shapes with higher genus. Criteria based on surface conformality and minimum description length are used to simultaneously identify the intrinsic global correspondence of the training data. The strength of the method is demonstrated by building a statistical model of the complex anatomical structure of the heart which includes atria, ventricles, aortic/pulmonary out How tracts, pulmonary veins/arteries, and superior/inferior vena cavae. The analysis of variance and leave-one-out-crossvalidation indicate that the derived model not only captures physiologically plausible modes of variation but also is robust and concise, thus greatly enhancing its potential clinical value. With this thesis, we also demonstrate how the derived dynamic statistical shape model can be used for 4D cardiac image segmentation and combined MR/CFD haemodynamic modelling.