Graph convolutional networks (GCNs) are a type of deep learning model designed to process graph-structured data. This review provides a comprehensive overview of GCNs, discussing their theoretical foundations, various types, applications, and challenges. GCNs are particularly useful for capturing the structural relationships among data points, which is essential for tasks such as node classification, link prediction, and graph classification. The review categorizes GCNs into spectral-based and spatial-based methods. Spectral-based methods rely on graph Fourier transforms and eigenvalues of the graph Laplacian, while spatial-based methods aggregate node information from the node's neighborhood. The review also discusses the challenges in GCNs, such as computational complexity, scalability, and the need for efficient training methods. Additionally, it highlights recent advancements in GCNs, including the use of Chebyshev polynomials, Cayley polynomials, and LanczosNet for efficient graph convolutions. The review also covers various applications of GCNs in computer vision, natural language processing, and other domains. Despite their potential, GCNs still face challenges in handling large-scale graphs and capturing complex patterns. The review concludes with future research directions, emphasizing the need for more efficient and scalable GCN models.Graph convolutional networks (GCNs) are a type of deep learning model designed to process graph-structured data. This review provides a comprehensive overview of GCNs, discussing their theoretical foundations, various types, applications, and challenges. GCNs are particularly useful for capturing the structural relationships among data points, which is essential for tasks such as node classification, link prediction, and graph classification. The review categorizes GCNs into spectral-based and spatial-based methods. Spectral-based methods rely on graph Fourier transforms and eigenvalues of the graph Laplacian, while spatial-based methods aggregate node information from the node's neighborhood. The review also discusses the challenges in GCNs, such as computational complexity, scalability, and the need for efficient training methods. Additionally, it highlights recent advancements in GCNs, including the use of Chebyshev polynomials, Cayley polynomials, and LanczosNet for efficient graph convolutions. The review also covers various applications of GCNs in computer vision, natural language processing, and other domains. Despite their potential, GCNs still face challenges in handling large-scale graphs and capturing complex patterns. The review concludes with future research directions, emphasizing the need for more efficient and scalable GCN models.