Graph Neural Networks (GNNs) represent a significant advancement in machine learning, specifically designed to address the complexities of analyzing non-Euclidean data structures like graphs, where relationships and interdependencies are intricate. GNNs extend the capabilities of neural networks to perform node-level, edge-level, and graph-level predictions, overcoming the limitations of Convolutional Neural Networks (CNNs) which are adept at processing regular grid-like data such as images. The article delves into the theoretical foundations of GNNs, discusses how they generalize the concept of convolution to graph data, and highlights their ability to maintain invariance to node ordering. It also explores practical applications of GNNs across various domains, including computer vision, natural language processing, traffic forecasting, and chemistry, where they help solve complex problems such as node classification, graph classification, and link prediction. Furthermore, the article outlines advancements like Graph Convolutional Networks (GCNs) and GraphSAGE, which enhance the ability to infer and learn from graph-based data, and touches upon the broad spectrum of fields where GNNs are being applied, emphasizing their potential in transforming how graph-structured data is processed and analyzed.