Audio-visual correlation learning aims to capture essential correspondences and understand natural phenomena between audio and video. With the rapid growth of deep learning, an increasing amount of attention has been paid to this emerging research issue. Through the past few years, various methods and datasets have been proposed for audio-visual correlation learning, which motivate us to conclude a comprehensive survey. This survey paper focuses on state-of-the-art (SOTA) models used to learn correlations between audio and video, but also discusses some tasks of definition and paradigm applied in AI multimedia. In addition, we investigate some objective functions frequently used for optimizing audio-visual correlation learning models and discuss how audio-visual data is exploited in the optimization process. Most importantly, we provide an extensive comparison and summarization of the recent progress of SOTA audio-visual correlation learning and discuss future research directions.