  We use global fits to analyze the most recent Higgs data from ATLAS, CMS and
Tevatron and compare the Standard Model (SM) prediction with natural extensions
of the SM. In particular we study wide classes of composite Higgs models based
on different coset structures (leading at low energy to different Higgs sectors
including extra singlets and Higgs doublets) and different coupling structures
of the elementary fermions to the strong sector. We point out in what
situations the composite models could improve (or worsen) the fit to the data
and compare with similar trends in the MSSM.
