We summarise highlights from an ongoing research programme that aims, in the long run, at
the ambitious goal of building a realistic, complete holographic composite-Higgs model.
This contribution focuses on vacuum misalignment, by showing how to unify
its description, as a phenomenon
arising from weak coupling considerations,
in the holographic description of a strongly coupled field theory in terms of a dual gravity theory.
This is achieved by a non-trivial treatment of boundary-localised terms in the gravity action.
The gravity backgrounds considered are completely regular and smooth.
We provide numerical examples showing that the mass spectrum of particles in the four-dimensional theory is free of pathologies, and
that a small hierarchy arises naturally, between the light states that, in this simplified set up, are analogous to
the standard-model particles, and all the other, new composite states emerging in the strongly coupled theory.