Popper

I don’t know if anyone does, but I think his criterion is considered by many to be too strong. Having one refutation doesn’t make us throw away a well-founded theory (as Kuhn wrote, only when there are a large number of problems does one change paradigm). Furthermore, refutation always involves assumptions (and therefore it is almost always possible to offer ad hoc solutions to say that the theory has not really been refuted in this case).
In general, it is difficult to give a sharp definition to complex concepts like science. It is a combination of all sorts of criteria in loose doses. The concepts need to be clear, the content of the claims needs to be sharp (i.e. what they are intended to infer), and hence it needs to have predictions that can be tested. It needs to be complex enough (the theory that if you hit someone it hurts is scientific but not really complex and I wouldn’t call it scientific), and to introduce a sufficient amount of empirical phenomena. That’s about it.