Abstract: As one of the most promising paradigms of integrated circuit design, the approximate circuit has aroused widespread concern in the scientific community. It takes advantage of the inherent error tolerance of some applications and relaxes the accuracy for reductions in area and power consumption. This paper aims to provide a comprehensive survey of reliability issues related to approximate circuits, which covers three concerns: error characteristic analysis, reliability and test, and reliable design involving approximate circuits. The error characteristic analysis is used to compare the outputs of the approximate circuit with those of its precise counterpart, which can help to find the most appropriate approximate design for a specific application in the large design space. With the approximate design getting close to physical realization, manufacturing defects and operational faults are inevitable; therefore, the reliability prediction and vulnerability test become increasingly important. However, the research on approximate circuit reliability and test is insufficient and needs more attention. Furtherly, although there is some existing work combining the approximate design with fault tolerant techniques, the reliability-enhancement approaches for approximate circuits are lacking.