Composite Higgses

We present an overview of composite Higgs models in light of the discovery of the Higgs boson. The small value of the physical Higgs mass suggests that the Higgs quartic is likely loop generated, thus models with tree-level quartics will generically be more tuned. We classify the various models (including bona fide composite Higgs, little Higgs, holographic composite Higgs, twin Higgs and dilatonic Higgs) based on their predictions for the Higgs potential, review the basic ingredients of each of them, and quantify the amount of tuning needed, which is not negligible in any model. We explain the main ideas for generating flavor structure and the main mechanisms for protecting against large flavor violating effects, and present a summary of the various coset models that can result in realistic pseudo-Goldstone Higgses. We review the current experimental status of such models by discussing the electroweak precision, flavor and direct search bounds, and comment on UV completions and on ways to incorporate dark matter.