With the development of information technologies and Internet of things (IoT) technologies,there are more and more scenarios under continual monitoring, such as transportation monitoring, disease monitoring, smart infrastructure etc. In these scenarios, how to protect the privacy of continuous sharing data is facing major challenges. Differential privacy is arigorous and provable privacy definition. Earlier research on differential privacy has focused on “one-shot” release on a static dataset. However, differential privacy under continual observation focuses on the continuous computationon the dynamic dataset. Now it has become one of the research hotspots. This study surveys the state-of-the-art techniqueson differential privacy under continual observation, and focuses on summarizing existing schemes that provide event-levelprivacy, user-levelprivacy, and w-event privacy. Following a comprehensive comparison and analysis of existing techniques, further research prospectsare put forward.