  Naturalness has for many years been a guiding principle in the search for
physics beyond the Standard Model, particularly for understanding the physics
of electroweak symmetry breaking. However, the discovery of the Higgs particle
at 125 GeV, accompanied by exclusion of many types of new physics expected in
natural models has called the principle into question. In addition, apart from
the scale of weak interactions, there are other quantities in nature which
appear unnaturally small and for which we have no proposal for a natural
explanation.We first review the principle, and then discuss some of the
conjectures which it has spawned. We then turn to some of the challenges to the
naturalness idea and consider alternatives.
