Deep learning-based 3-dimensional (3D) shape reconstruction from 2-dimensional (2D) magnetic resonance imaging (MRI) has become increasingly important in medical disease diagnosis, treatment planning, and computational modeling. This review surveys the methodological landscape of 3D MRI reconstruction, focusing on 4 primary approaches: point cloud, mesh-based, shape-aware, and volumetric models. For each category, we analyze the current state-of-the-art techniques, their methodological foundation, limitations, and applications across anatomical structures. We provide an extensive overview ranging from cardiac to neurological to lung imaging. We also focus on the clinical applicability of models to diseased anatomy, and the influence of their training and testing data. We examine publicly available datasets, computational demands, and evaluation metrics. Finally, we highlight the emerging research directions including multimodal integration and cross-modality frameworks. This review aims to provide researchers with a structured overview of current 3D reconstruction methodologies to identify opportunities for advancing deep learning towards more robust, generalizable, and clinically impactful solutions.