Modern deep learning developments create new opportunities for 3D mapping technology, scene reconstruction pipelines, and virtual reality development. Despite advances in 3D deep learning technology, direct training of deep learning models on 3D data faces challenges due to the high dimensionality inherent in 3D data and the scarcity of labeled datasets. Structure-from-motion (SfM) and Simultaneous Localization and Mapping (SLAM) exhibit robust performance when applied to structured indoor environments but often struggle with ambiguous features in unstructured environments. These techniques often struggle to generate detailed geometric representations effective for downstream tasks such as rendering and semantic analysis. Current limitations require the development of 3D representation methods that combine traditional geometric techniques with deep learning capabilities to generate robust geometry-aware deep learning models. The dissertation provides solutions to the fundamental challenges in 3D vision by developing geometric deep learning methods tailored for essential tasks such as camera pose estimation, point cloud registration, depth prediction, and 3D reconstruction. The integration of geometric priors or constraints, such as including depth information, surface normals, and equivariance into deep learning models, enhances both the accuracy and robustness of geometric representations. This study systematically investigates key components of 3D vision, including camera pose estimation, point cloud registration, depth estimation, and high-fidelity 3D reconstruction, demonstrating their effectiveness across real-world applications such as digital cultural heritage preservation and immersive VR/AR environments.