For the past few years, the Consumer Internet of Things (CIoT) has entered public lives. While CIoT has improved the convenience of people's daily lives, it has also brought new security and privacy concerns. In this survey, we try to figure out what researchers can learn about the security and privacy of CIoT by traffic analysis, a popular method in the security community. From the security and privacy perspective, this survey seeks out the new characteristics in CIoT traffic analysis, the state-of-the-art progress in CIoT traffic analysis, and the challenges yet to be solved. We collected 310 papers from January 2018 to December 2023 related to CIoT traffic analysis from the security and privacy perspective and summarized the process of CIoT traffic analysis in which the new characteristics of CIoT are identified. Then, we detail existing works based on five application goals: device fingerprinting, user activity inference, malicious traffic analysis, security analysis, and measurement. At last, we discuss the new challenges and future research directions.