Nowadays, more and more news readers read news online where they have access to millions of news articles from multiple sources. In order to help users find the right and relevant content, news recommender systems (NRS) are developed to relieve the information overload problem and suggest news items that might be of interest for the news readers. In this paper, we highlight the major challenges faced by the NRS and identify the possible solutions from the state-of-the-art. Our discussion is divided into two parts. In the first part, we present an overview of the recommendation solutions, datasets, evaluation criteria beyond accuracy and recommendation platforms being used in the NRS. We also talk about two popular classes of models that have been successfully used in recent years. In the second part, we focus on the deep neural networks as solutions to build the NRS. Different from previous surveys, we study the effects of news recommendations on user behaviors and try to suggest possible remedies to mitigate those effects. By providing the state-ofthe-art knowledge, this survey can help researchers and professional practitioners have a better understanding of the recent developments in news recommendation algorithms. In addition, this survey sheds light on the potential new directions.