In computer architecture research and development, simulation is a powerful way of acquiring and predicting processor behaviors. While architectural simulation has been extensively utilized for computer performance evaluation, design space exploration, and computer architecture assessment, it still suffers from the high computational costs in practice. Specifically, the total simulation time is determined by the simulator's raw speed and the total number of simulated instructions. The simulator's speed can be improved by enhanced simulation infrastructures (e.g., simulators with high-level abstraction, parallel simulators, and hardware-assisted simulators). Orthogonal to these work, recent studies also managed to significantly reduce the total number of simulated instructions with a slight loss of accuracy. Interestingly, we observe that most of these work are built upon statistical techniques. This survey presents a comprehensive review to such studies and proposes a taxonomy based on the sources of reduction. In addition to identifying the similarities and differences of state-of-the-art approaches, we further discuss insights gained from these studies as well as implications for future research.