Air pollution is an important factor affecting public health, and air quality prediction is the key to air pollution early warning and a hot research topic in the fields of environmental science, statistics, and computer science in recent years. This study reviews the research status and progress of air quality prediction methods, with a special focus on the systematical analysis and summarization of the applications of the newly-emerged deep learning methods in recent years in air quality prediction. Specifically, the evolution process of air quality prediction methods and air pollution datasets are outlined. After the traditional air quality prediction methods are described, the progress of existing deep learning-based air quality prediction methods is analyzed and compared in detail from the perspectives of temporal information, temporal-spatial information, and attention mechanisms. Finally, the development trend of air quality prediction methods is summarized and predicted.