The discovery of a Higgs-like scalar particle with a mass of 125 GeV
has reinforced the need to address the gauge hierarchy problem: in the
absence of supersymmetry, a fundamental scalar particle would require
an unnatural amount of fine-tuning. This problem can be solved if the
Higgs is a composite particle of a new strong interaction, in
particular if it arises as a pseudo Nambu-Goldstone boson. But even
then, a moderate degree of fine-tuning calls for relatively light
fermionic resonances. Apart from direct searches for such resonances,
such models are strongly constrained by electroweak precision
observables and flavour physics. I will present an overview of
electroweak, flavour and collider constraints on composite Higgs
models, considering several choices for the electroweak
representations, comparing flavour-symmetric models to
flavour-anarchic ones and identifying the least fine-tuned cases and
their prospects.
