Recent improvements in non-invasive imaging, together with the introduction of fully-automated segmentation algorithms and big data analytics, has paved the way for large-scale population-based imaging studies. These studies promise to increase our understanding of a large number of medical conditions, including cardiovascular diseases. However, analysis of cardiac shape in such studies is often limited to simple morphometric indices, ignoring large part of the information available in medical images. Discovery of new biomarkers by machine learning has recently gained traction, but often lacks interpretability. The research presented in this thesis aimed at developing novel explainable machine learning and computational methods capable of better summarizing shape variability, to better inform association and predictive clinical models in large-scale imaging studies. A powerful and flexible framework to model the relationship between three-dimensional (3D) cardiac atlases, encoding multiple phenotypic traits, and genetic variables is first presented. The proposed approach enables the detection of regional phenotype-genotype associations that would be otherwise neglected by conventional association analysis. Three learning-based systems based on deep generative models are then proposed. In the first model, I propose a classifier of cardiac shapes which exploits task-specific generative shape features, and it is designed to enable the visualisation of the anatomical effect these features encode in 3D, making the classification task transparent. The second approach models a database of anatomical shapes via a hierarchy of conditional latent variables and it is capable of detecting, quantifying and visualising onto a template shape the most discriminative anatomical features that characterize distinct clinical conditions. Finally, a preliminary analysis of a deep learning system capable of reconstructing 3D high-resolution cardiac segmentations from a sparse set of 2D views segmentations is reported. This thesis demonstrates that machine learning approaches can facilitate high-throughput analysis of normal and pathological anatomy and of its determinants without losing clinical interpretability.