Recommendation system can effectively address the problem of information overload, attracting extensive attention from both academia and industry. Collaborative filtering recommender algorithms based on graph neural networks have emerged as a widely adopted technique in recent years. These algorithms can effectively represent user and item features and learn intricate relationships between users and items. Therefore, they have become prevalent in the field of recommendation system. Firstly, the paper categorizes the algorithms based on the problems that they aim to solve and then provides a comparison and analysis of representative algorithms within each category. The paper also summarize commonly used datasets in experiments and briefly introduce the key evaluation metrics. Finally, the paper discuss the challenges and potential research directions.