Statistical shape modeling (SSM) is emerging as an important tool in medical image analysis, allowing for population-based quantitative evaluation of morphometrics. SSM enables objective clinical hypothesis testing where anatomical shape variation is related to biological function and outcomes. The traditional pipeline for correspondence-based SSM construction has significant limitations and requires painstaking and cost-prohibitive steps. This dissertation builds upon recent developments in Bayesian machine learning and computer vision to streamline the adoption of SSM in biomedical research and practice by reducing construction burdens and broadening potential applications and use cases. Additionally, this work focuses on important clinical considerations in deep learning model deployment, such as prediction trustworthiness and robustness to data scarcity. The contributions of this work include novel frameworks that (1) predict SSM from medical images with reliable and calibrated uncertainty quantification, (2) provide dynamic or longitudinal SSM from 4D spatiotemporal data, and (3) learn SSM in an unsupervised manner from imperfect, lightweight point cloud shape representations. These efforts significantly reduce the required costs and manual labor associated with constructing anatomical SSM, helping SSM become a more viable clinical tool to advance medical practice and accessibility.