The tthh production at colliders contains rich information on the nature of the Higgs boson. In this article, we systematically studied its physics at the high-luminosity Large Hadron Collider (HL-LHC), using exclusive channels with multiple (≥ 5) b-jets and one lepton (5b1l), multiple (≥ 5) b-jets and opposite-sign dilepton (5b2l), same-sign dilepton (SS2l), multiple leptons (multi-l), and ditau resonance (ττ). The scenarios analyzed include: (1) the tthh production in Standard Model; (2) the tthh production mediated by anomalous cubic Higgs self-coupling and tthh contact interaction; (3) heavy Higgs (H) production with ttH → tthh; and (4) pair production of fermionic top partners (T) with TT → tthh. To address the complication of event topologies and the mess of combinatorial backgrounds, a tool of boosted-decision-tree was applied in the analyses. The 5b1l and SS2l analyses define the two most promising channels. For the nonresonant tthh production, a combination of these exclusive analyses allows for its measurement in the SM with a statistical significance ∼0.9σ (with S=B > 1%), and may partially break the sensitivity degeneracy with respect to a varying cubic Higgs self-coupling, a difficulty usually thought to exist in gluon fusion di-Higgs analysis at HL-LHC. These sensitivities were also projected to future hadron colliders at 27 TeV and 100 TeV. For the resonant tthh productions, the heavy Higgs boson in type II two-Higgs-doublet-model could be efficiently searched for between the mass thresholds 2m h < m H < 2m t and even beyond that, for relatively small tan β (vacuum alignment), while the fermionic top partners in composite Higgs models could be probed up to ∼1.5 TeV and ∼1.7 TeV, for BrðT → thÞ ¼ 25% and 50%, respectively.