The Recommender system is a vital information service on today's Internet. Recently, graph neural networks have emerged as the leading approach for recommender systems. We try to review recent literature on graph neural network-based recommender systems, covering the background and development of both recommender systems and graph neural networks. Then categorizing recommender systems by their settings and graph neural networks by spectral and spatial models, we explore the motivation behind incorporating graph neural networks into recommender systems. We also analyze challenges and open problems in graph construction, embedding propagation and aggregation, and computation efficiency. This guides us to better explore the future directions and developments in this domain.