This paper provides a comprehensive survey of geometric graph neural networks (GNNs), focusing on data structures, models, and applications. Geometric graphs, which incorporate geometric features such as 3D coordinates, are essential for modeling scientific problems like physics and biochemistry. Unlike generic graphs, geometric graphs exhibit symmetries such as translations, rotations, and reflections, which current GNNs struggle to handle effectively. To address this, researchers have developed various GNNs with invariant and equivariant properties to better capture the geometry and topology of geometric graphs. The survey begins with an introduction to symmetry concepts, including groups, group representations, and equivariance/invariance. It then defines geometric graphs and their transformations, distinguishing them from regular graphs. The paper categorizes existing GNN models into invariant GNNs and equivariant GNNs, with further subcategories based on scalarization and high-degree steerable models. Examples of these models, such as SchNet, DimeNet, GemNet, and EGNN, are discussed in detail. The survey also highlights the applications of geometric GNNs in various scientific domains, including physical dynamics simulation, molecular property prediction, protein structure prediction, and RNA structure ranking. It provides a taxonomy of geometric GNNs and discusses the challenges and future directions in the field. Finally, the paper emphasizes the importance of geometric GNNs for processing complex data structures and their potential in advancing scientific research.This paper provides a comprehensive survey of geometric graph neural networks (GNNs), focusing on data structures, models, and applications. Geometric graphs, which incorporate geometric features such as 3D coordinates, are essential for modeling scientific problems like physics and biochemistry. Unlike generic graphs, geometric graphs exhibit symmetries such as translations, rotations, and reflections, which current GNNs struggle to handle effectively. To address this, researchers have developed various GNNs with invariant and equivariant properties to better capture the geometry and topology of geometric graphs. The survey begins with an introduction to symmetry concepts, including groups, group representations, and equivariance/invariance. It then defines geometric graphs and their transformations, distinguishing them from regular graphs. The paper categorizes existing GNN models into invariant GNNs and equivariant GNNs, with further subcategories based on scalarization and high-degree steerable models. Examples of these models, such as SchNet, DimeNet, GemNet, and EGNN, are discussed in detail. The survey also highlights the applications of geometric GNNs in various scientific domains, including physical dynamics simulation, molecular property prediction, protein structure prediction, and RNA structure ranking. It provides a taxonomy of geometric GNNs and discusses the challenges and future directions in the field. Finally, the paper emphasizes the importance of geometric GNNs for processing complex data structures and their potential in advancing scientific research.