This paper provides a comprehensive review of graph convolutional networks (GCNs), a prominent class of deep learning models designed to handle graph-structured data. The authors categorize existing GCN models into two main types: spectral-based and spatial-based, and discuss their applications in various domains. Spectral-based GCNs use graph Fourier transform to define convolutions in the spectral domain, while spatial-based GCNs focus on aggregating node representations from neighborhoods in the vertex domain. The paper highlights the advantages and limitations of these models, such as computational complexity and localization properties. It also reviews specific models like ChebNet, GCN, FastGCN, and GraphSAGE, and discusses their extensions and variants. Additionally, the paper explores applications of GCNs in computer vision, natural language processing, and other fields, emphasizing their effectiveness in tasks like image classification, video action recognition, point cloud segmentation, and text classification. Finally, the authors identify open challenges and suggest future research directions, including the need for more efficient training methods and deeper models.This paper provides a comprehensive review of graph convolutional networks (GCNs), a prominent class of deep learning models designed to handle graph-structured data. The authors categorize existing GCN models into two main types: spectral-based and spatial-based, and discuss their applications in various domains. Spectral-based GCNs use graph Fourier transform to define convolutions in the spectral domain, while spatial-based GCNs focus on aggregating node representations from neighborhoods in the vertex domain. The paper highlights the advantages and limitations of these models, such as computational complexity and localization properties. It also reviews specific models like ChebNet, GCN, FastGCN, and GraphSAGE, and discusses their extensions and variants. Additionally, the paper explores applications of GCNs in computer vision, natural language processing, and other fields, emphasizing their effectiveness in tasks like image classification, video action recognition, point cloud segmentation, and text classification. Finally, the authors identify open challenges and suggest future research directions, including the need for more efficient training methods and deeper models.