In recent years, graph convolutional networks (GCNs) have gained widespread attention and applications in image classification tasks. While traditional convolutional neural networks (CNNs) usually represent images as a two-dimensional grid of pixels when processing image data, the classical model of graph neural networks (GNNs), GCNs, can effectively handle data with graph structure, such as social networks, recommender systems, and molecular structures. In this paper, we will introduce the problems that graph convolutional networks have had, such as over-smoothing, and the methods to solve them, and suggest some possible future directions.