  Many compelling theories to address the Higgs hierarchy problem predict
strong interactions between the top and a sector of New Physics. In minimal
composite Higgs models (CHM), the top interactions with a BSM
strongly-interacting sector give the leading contribution to trigger the EWSB
and generate a light mass for the pseudo-NG Higgs. This implies that new
composite states (vector-like top-partners, composite vector resonances, new
composite scalars) dominantly interact with third-generation quarks and, when
produced at colliders, generate top quarks in the final state. I will indicate
interesting signatures involving top quarks for CHM discovery/test at the LHC
and future colliders.
