Autonomous driving has become one of the most revolutionary innovations in the field of transportation. Its extensive application prospect drives many manufacturers to develop and deploy autonomous vehicles on public roads. However, given the fact that traffic accidents involving autonomous vehicles continue to occur, safety has become the main obstacle for their widespread adoption. To tackle this issue, simulation-based fuzzing is gaining attention due to its capability to automatically identify flaws of autonomous driving systems which may cause traffic accidents. However, this technology is still in its early stages of research, and existing work are far from faithfully addressing the potential safety issues of autonomous driving systems. Considering this, we first introduce the basic architecture and research status of this technology. After that, we summarize the shortcomings of existing work, as well as the challenges to achieve effective simulation-based fuzzing. Accordingly, we try to propose solutions which can potentially tackle these challenges. To showcase the effectiveness of these solutions, we apply them in the safety assessment of popular open-source autonomous driving systems (i.e., Apollo and Autoware). Results show that, these solutions can boost the capability of existing simulation-based fuzzers in identifying and diagnosing safety-related flaws of Apollo and Autoware. Finally, we try to pinpoint the future research directions, so as to ease follow-up research.