The automotive industry has witnessed an increasing level of development in the past decades; from manufacturing manually operated vehicles to manufacturing vehicles with a high level of automation. With the recent developments in Artificial Intelligence (AI), automotive companies now employ blackbox AI models to enable vehicles to perceive their environments and make driving decisions with little or no input from a human. With the hope to deploy autonomous vehicles (AV) on a commercial scale, the acceptance of AV by society becomes paramount and may largely depend on their degree of transparency, trustworthiness, and compliance with regulations. The assessment of the compliance of AVs to these acceptance requirements can be facilitated through the provision of explanations for AVs' behaviour. Explainability is therefore seen as an important requirement for AVs. AVs should be able to explain what they have 'seen', done, and might do in environments in which they operate. In this paper, we provide a comprehensive survey of the existing body of work around explainable autonomous driving. First, we open with a motivation for explanations by highlighting and emphasising the importance of transparency, accountability, and trust in AVs; and examining existing regulations and standards related to AVs. Second, we identify and categorise the different stakeholders involved in the development, use, and regulation of AVs and elicit their explanation requirements for AV. Third, we provide a rigorous review of previous work on explanations for the different AV operations (i.e., perception, localisation, planning, control, and system management). Finally, we identify pertinent challenges and provide recommendations, such as a conceptual framework for AV explainability. This survey aims to provide the fundamental knowledge required of researchers who are interested in explainability in AVs.