  Twin Higgs models are the prime illustration of neutral naturalness, where
the new particles of the twin sector, gauge singlets of the Standard Model
(SM), ameliorate the little hierarchy problem. In this work, we analyse
phenomenological implications of the heavy Higgs of the Mirror Twin Higgs and
Fraternal Twin Higgs models, when electroweak symmetry breaking is linearly
realized. The most general structure of twin Higgs symmetry breaking, including
explicit soft and hard breaking terms in the scalar potential, is employed. The
direct and indirect searches at the LHC are used to probe the parameter space
of Twin Higgs models through mixing of the heavy Higgs with the SM Higgs and
decays of the heavy Higgs to the SM states. Moreover, for the Fraternal Twin
Higgs, we study the production and decays of twin glueball and bottomonium
states to the SM light fermions, which have interesting signatures involving
displaced vertices and are potentially observable at the colliders.
