Abstract: Query suggestion (QS) is an indispensable part of search engines. It can provide query candidates before users entering a complete query to help express their information needs more accurately and more quickly. Deep learning helps to improve the accuracy of QS and it has become the mainstream technology to promote the development of QS in recent years. We mainly summarize, analyze and compare the research status of deep learning based QS (DQS). According to the different application stages of deep learning, DQS methods are divided into two categories: generative QS methods and ranking-based QS suggestion methods, and the modeling ideas of each model are analyzed. In addition, the data sets, baselines and evaluation indexes commonly used in the field of QS are introduced, and the technical characteristics and experimental results of different models are compared. Finally, the current challenges and future development trends of QS research based on deep learning are summarized.