Due to researchers'aim to study personalized recommendations for different business fields, the summary of recommendation methods in specific fields is of practical significance. News recommendation systems were the earliest research field regarding recommendation systems, and were also the earliest recommendation field to apply the collaborative filtering method. In addition, news is real-time and rich in content, which makes news recommendation methods more challenging than in other fields. Thus, this paper summarizes the research progress regarding news recommendation methods. From 2018 to 2020, developed news recommendation methods were mainly deep learning-based, attention-based, and knowledge graphs-based. As of 2020, there are many news recommendation methods that combine attention mechanisms and knowledge graphs. However, these methods were all developed based on basic methods (the collaborative filtering method, the content-based recommendation method, and a mixed recommendation method combining the two). In order to allow researchers to have a detailed understanding of the development process of news recommendation methods, the news recommendation methods surveyed in this paper, which cover nearly 10 years, are divided into three categories according to the abovementioned basic methods. Firstly, the paper introduces the basic ideas of each category of methods and then summarizes the recommendation methods that are combined with other methods based on each category of methods and according to the time sequence of research results. Finally, this paper also summarizes the challenges confronting news recommendation systems.