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When will automated vehicles come onto the market? This question has puzzled the automotive industry and society for years. The technology and its implementation have made rapid progress over the last decade, but the challenge of how to prove the safety of these systems has not yet been solved. Since a market launch without proof of safety would neither be accepted by society nor by legislators, much time and many resources have been invested into safety assessment in recent years in order to develop new approaches for an efficient assessment. This paper therefore provides an overview of various approaches, and gives a comprehensive survey of the so-called scenario-based approach. The scenario-based approach is a promising method, in which individual traffic situations are typically tested by means of virtual simulation. Since an infinite number of different scenarios can theoretically occur in real-world traffic, even the scenario-based approach leaves the question unanswered as to how to break these down into a finite set of scenarios, and find those which are representative in order to render testing more manageable. This paper provides a comprehensive literature review of related safety-assessment publications that deal precisely with this question. Therefore, this paper develops a novel taxonomy for the scenario-based approach, and classifies all literature sources. Based on this, the existing methods will be compared with each other and, as one conclusion, the alternative concept of formal verification will be combined with the scenario-based approach. Finally, future research priorities are derived.