No-go theorems: What are they good for?

No-go theorems have played an important role in the development and assessment of scientific theories. They have stopped whole research programmes and have given rise to strong ontological commitments. Given the importance they obviously have had in physics and philosophy of physics and the huge amount of literature on the consequences of specific no-go theorems, there has been relatively little attention to the more abstract assessment of no-go theorems as a tool in theory development. We will here provide this abstract assessment of no-go theorems and conclude that the methodological implications one may draw from no-go theorems are in disagreement with the implications that have often been drawn from them in the history of science.