Due to the inherent tolerance to inaccuracy in data-driven applications, approximate multipliers have received growing attentions for its compactness and energy efficiency. However, the energy efficiency of an approximate multiplier largely depends on how and where the inaccuracy is introduced into the design, which can be roughly categorized to 3 design levels: (1) architecture, (2) algorithm, and (3) circuit. Such large design space inevitably incurs design complexities and challenges in selecting the appropriate multiplier for a particular application. Thus, this paper provides a comprehensive review of the state-of-the-art (SOTA) designs of approximate multipliers for future investigations.