In the area of the foundations of quantum mechanics a true industry appears to have developed in the last decades, with the aim of proving as many results as possible concerning what there cannot be in the quantum realm. In principle, the significance of proving ‘no-go’ results should consist in clarifying the fundamental structure of the theory, by pointing out a class of basic constraints that the theory itself is supposed to satisfy. In the present paper I will discuss some (...) more recent no-go claims and I will argue against the deep significance of these results, with a two-fold strategy. First, I will consider three results concerning respectively local realism, quantum covariance and predictive power in quantum mechanics, and I will try to show how controversial the main conditions of the negative theorem turn out to be—something that strongly undermines the general relevance of these theorems. Second, I will try to discuss what I take to be a common feature of these theoretical enterprises, namely that of aiming at establishing negative results for quantum mechanics in absence of a deeper understanding of the overall ontological content and structure of the theory. I will argue that the only way toward such an understanding may be to cast in advance the problems in a clear and well-defined interpretational framework—which in my view means primarily to specify the ontology that quantum theory is supposed to be about—and after to wonder whether problems that seemed worth pursuing still are so in the framework. (shrink)