  Constraining the Higgs boson properties is a cornerstone of the LHC program
and future colliders. In this Snowmass contribution, we study the potential to
directly probe the Higgs-top CP-structure via the $t\bar{t}h$ production at the
HL-LHC, 100 TeV FCC and muon colliders. We find the limits on the CP phase
($\alpha$) at 95% CL are $|\alpha| \lesssim 36^\circ$ with dileptonic $t\bar t
(h\to b\bar b) $ and $|\alpha| \lesssim 25^\circ$ with combined $t\bar t (h\to
\gamma\gamma) $ at the HL-LHC. The 100 TeV FCC brings a significant improvement
in sensitivity with $|\alpha| \lesssim 3^\circ$ for the dileptonic $t\bar t
(h\to b\bar b) $, due to the remarkable gain in the signal cross-section and
the increased luminosity. At future muon colliders, we find that the bounds
with semileptonic $t\bar t (h\to b\bar b) \nu\bar\nu$ are $|\alpha| \lesssim
9^\circ$ for 10 TeV and $|\alpha| \lesssim 3^\circ$ for 30 TeV, respectively.
