The end-to-end learning pipeline is gradually creating a paradigm shift in the ongoing development of highly autonomous vehicles, largely due to advances in deep learning, the availability of large-scale training datasets, and improvements in integrated sensor devices. However, a lack of interpretability in real-time decisions with contemporary learning methods impedes user trust and attenuates the widespread deployment and commercialization of such vehicles. Moreover, the issue is exacerbated when these cars are involved in or cause traffic accidents. Such drawback raises serious safety concerns from societal and legal perspectives. Consequently, explainability in end-to-end autonomous driving is essential to build trust in vehicular automation. However, the safety and explainability aspects of end-to-end driving have generally been investigated disjointly by researchers in today's state of the art. This survey aims to bridge the gaps between these topics and seeks to answer the following research question: When and how can explanations improve safety of end-to-end autonomous driving? In this regard, we first revisit established safety and state-of-the-art explainability techniques in end-to-end driving. Furthermore, we present three critical case studies and show the pivotal role of explanations in enhancing self-driving safety. Finally, we describe insights from empirical studies and reveal potential value, limitations, and caveats of practical explainable AI methods with respect to their safety assurance in end-to-end autonomous driving.

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