Developing autonomous driving (AD) systems is challenging due to the complexity of the systems and the need to assure their safe and reliable operation. The widely adopted approach of DevOps seems promising to support the continuous technological progress in AI and the demand for fast reaction to incidents, which necessitate continuous development, deployment, and monitoring. We present a systematic literature review meant to identify, analyse, and synthesise a broad range of existing literature related to usage of DevOps in autonomous driving development. Our results provide a structured overview of challenges and solutions, arising from applying DevOps to safety-related AI-enabled functions. Our results indicate that there are still several open topics to be addressed to enable safe DevOps for the development of safe AD.