  The discovery of the Higgs boson has put considerable pressure on theories
that aim to solve the hierarchy problem. Scenarios in which the Higgs is a
pseudo Nambu-Goldstone boson (NGB) of some new strong dynamics must possess a
number of non-generic features in order to pass the progressively stringent
collider bounds and simultaneously meet our naturalness criteria. Among these
features are the existence of light fermionic partners of the top quark and an
efficient collective breaking of the Nambu-Goldstone symmetry. The top partners
have to be not only parametrically lighter than the other composites, but also
weakly coupled to them in order to suppress unwanted flavor-violating effects.
A Natural pseudo-NGB Higgs model should also be able to fit the LHC Higgs data
without fine-tuning. Among theories with comparable compositeness scales, those
that predict smaller corrections in the Higgs couplings to the standard model
particles are therefore preferred.
  A concrete implementation of these ingredients is discussed in a scenario
based on the coset SU(5)/SO(5). The fit to the current LHC Higgs data is
significantly improved compared to the minimal scenarios, and a fully natural
explanation of both the weak scale and the Higgs boson mass can be attained. An
important role is played by an independent quartic Higgs coupling generated by
UV-sensitive loops involving electroweak doublets mixing with the top partners.
The collider signature of this framework is shown to be rather model-dependent;
in particular, the exotic scalars can alter the phenomenology of the top
partners at a qualitative level.
