Quantum computing is expected to solve many classically difficult problems in theory. The rapid development of quantum computers in recent years is pushing the theory into practice. However, numerous errors in current hardware can cause incorrect computational results, severely limiting the ability of quantum computers to solve practical problems. Quantum computing system software lies between applications and hardware; tapping the full potential of system software in hardware error mitigation is crucial to realizing practical quantum computing in the near future. As a consequence, many research works on quantum computing system software have recently emerged. In this paper, we classify them into three categories: compilers, runtime systems and debuggers. Through in-depth analysis of these works, we sort out the research status of quantum computing system software, and reveal their important roles in hardware error mitigation. We also look forward to the future research directions.