No evidence of “new physics” was found so far by LHC experiments, and this situation has led some voices in the physics community to call for the abandonment of the “naturalness” criterion, while other scientists have felt the need to break a lance in its defense by claiming that, at least in some sense, it has already led to successes and therefore should not be dismissed too quickly, but rather only reflected or reshaped to fit new needs. In our paper we will argue that present pro-or-contra naturalness debates miss the fundamental point that naturalness, despite contrary claims, is essentially a very hazily defined, in a sense even mythical notion which, in the course of more than four decades, has been steadily, and often not coherently, shaped by its interplay with different branches of model-building in high-energy physics and cosmology on the one side, and new incoming experimental results on the other. In our paper we will endeavor to clear up some of the physical and philosophical haze by taking a closer look back at (real or alleged) origin of naturalness in the 1970s and 1980s, with particular attention to the early work of Kenneth Wilson. In doing this, we aim to bring to light how naturalness belongs to a long tradition of present and past physical and philosophical criteria for effectively guiding theoretical reflection and experimental practice in fundamental research.