Secure data deletion is the task of deleting data irrecoverably from a physical medium. In the digital world, data is not securely deleted by default; instead, many approaches add secure deletion to existing physical medium interfaces. Interfaces to the physical medium exist at different layers, such as user-level applications, the file system, the device driver, etc. Depending on which interface is used, the properties of an approach can differ significantly. In this paper, we survey the related work in detail and organize existing approaches in terms of their interfaces to physical media. We further present a taxonomy of adversaries differing in their capabilities as well as a systematization for the characteristics of secure deletion approaches. Characteristics include environmental assumptions, such as how the interface's use affects the physical medium, as well as behavioural properties of the approach such as the deletion latency and physical wear. We perform experiments to test a selection of approaches on a variety of file systems and analyze the assumptions made in practice.