In design science research (DSR), designs create utility by providing a working solution to a relevant problem. While solution instances usually are associated with a unique, contextualized problem, models or methods should be applicable to larger numbers of problems that share certain characteristics. Ultimately, design principles or design theories claim utility by being applicable to very broad problem classes. We show that most designs exist on many levels of abstraction. Problem classes may have different range and variety, and solution artefacts may be applicable to problem classes of different sizes. Consequently, design researchers need to understand abstraction as an important characteristic of problems and solutions, and they need guidance on how to navigate abstraction levels during the design process. Informed by the concept of abstraction in disciplines such as management and computer science, we demonstrate how important DSR artefact types look like on different levels of abstraction. This allows us to generalize abstraction for DSR and specify elementary operations to increase or reduce the abstraction level of problems, solutions, and designs. The analysis of how selected DSR methods are traversing abstraction levels provides the backdrop for discussing which guidelines are needed for dealing with abstraction in DSR and when to apply the proposed abstraction-related operations.