Over the past two decades, several methods have been developed to evaluate the societal impact of research. Compared to the practical development of the field, the conceptual development is relatively weak. This review article contributes to the latter by elucidating the theoretical aspects of the dominant methods for evaluating societal impact of research, in particular, their presuppositions about the relationship between scientific and societal value of research. We analyse 10 approaches to the assessment of the societal impact of research from a constructivist perspective. The methods represent different understandings of knowledge exchange, which can be understood in terms of linear, cyclical, and co-production models. In addition, the evaluation methods use a variety of concepts for the societal value of research, which suggest different relationships with scientific value. While some methods rely on a clear and explicit distinction between the two types of value, other methods, in particular Evaluative Inquiry, ASIRPA, Contribution Mapping, Public Value Mapping, and SIAMPI, consider the mechanisms for producing societal value integral to the research process. We conclude that evaluation methods must balance between demarcating societal value as a separate performance indicator for practical purposes and doing justice to the (constructivist) science studies' findings about the integration of scientific and societal value of research. Our analytic comparison of assessment methods can assist research evaluators in the conscious and responsible selection of an approach that fits with the object under evaluation. As evaluation actively shapes knowledge production, it is important not to use oversimplified concepts of societal value.