Graph neural networks (GNN) have become a powerful framework for analyzing structured data in the form of graphs, with applications spanning diverse fields such as social networks, biology, recommender systems, etc. This survey explores methodology, development, and advances in GNN architectures. We methodically survey the major classes of GNNs, including Convolutional GNNs (ConvGNNs), Spatial-Temporal Graph Neural Networks (STGNNs), Recurrent-based GNNs (RecGNNs), and Graph Autoencoders (GAEs). Every model is discussed in terms of underlying mathematical formulations, design principles, and practical applications. This survey goals to supply a comprehensive conception of GNNs for practitioners and researchers alike, highlighting their versatility and potential for future innovations in graph neural networks. We will furthermore discuss applications of graph neural networks across different fields and epitomize open-source codes, benchmark datasets, and model valuation for graph neural networks. In the end, this survey specifies existing challenges in interpretability, generalization, and scalability and proposes possible future research trends to further promote the performance of GNNs across various graph-based learning missions.