Autonomous Systems are seeing increasing use and increasingly safety-significant application. Consequently, the safety of autonomous systems is an important topic. To reflect this importance the Safety Critical Systems Club (SCSC) has established the Safety of Autonomous Systems Working Group (SASWG). This paper introduces the SASWG and describes (and justifies) the approach it is taking. A running example is used to illustrate challenges, which are organised against three “difficulty horizons”. Potential solutions to some of the challenges are outlined; possible research directions are suggested for other challenges. Some proposed but invalid solutions are also identified. Overall, whilst the SASWG acknowledges the very significant benefits that could accrue from autonomous systems, it believes their development and implementation should be pursued carefully and thoughtfully.