This entry is about the notion of naturalness in (particle-)physics. For the notion in mathematics see at natural transformation. In (particle-)physics the term “naturalness” [‘t Hooft 1980, Gell- Mann 1983] refers to the vague idea that a model of physics is expected to work without requiring unlikely-looking ad-hoc coincidences or “fine-tuning” of its parameters (such as the choice of renormalization constants), and that instead all such “conspiracies” among parameter values are to have some systematic cause, such as some (broken) symmetry of the model. An archetypical example, which at times has been referred to as the naturalness probem of the standard model of particle physics, is that the mass of the Higgs boson is first of all many orders of magnitude below the Planck scale, while at the same time potentially receiving very large potential quantum corrections from the presence of (potentially undetected) heavy particles, which therefore must coincidentally cancel out. This is also called the hierarchy problem. Accordingly, a popular suggestion has been that there should be a symmetry in nature which is to naturally explain this otherwise coincidental cancellation, namely low-energy supersymmetry. The failure of such a symmetry to be observed at the LHC experiment is leading the high energy physics community to a re-examination of the naturalness paradigm and/or to focus on alternative mechanisms, such as a composite Higgs boson. The next main example of (lack of) naturalness often considered is the cosmological constant (dark energy), which seems tiny when compared to the quantum corrections which it naively receives from the vacuum energy of all fields in the observable universe. A key problem is arguably that the principle of naturalness has been used in a very vague and very ambiguous sense. Even apart from the problem of which large or small numbers are to be regarded as “unlikely” (see the quote below from Wilson 04), there is technical fine print. Both...