Approximate computing is an advanced computational technique that trades the accuracy of computation results for better utilization of system resources. It has emerged as a new preferable paradigm over traditional computing architectures for many applications where inaccurate results are acceptable. However, approximate computing also introduces security vulnerabilities mainly due to the fact that the uncertain and unpredictable intrinsic errors during approximate execution may be indistinguishable from malicious modification of the input data, the execution process, and the results. On the other hand, interestingly, approximate computing presents new opportunities to secure the system and the computation. Existing work on the security of approximate computing covers threat models, countermeasures, and evaluations but lacks a framework for analysis and comparison. In this article, we provide a classification of the state-of-the-art works in this research field, including threat models in approximate computing and promising security approaches using approximate computing. Open questions and potential future research directions are also discussed.