  We implement a comprehensive and detailed study of the alignment of Yukawa
couplings in the so-called Higgs basis taking the framework of general two
Higgs doublet models (2HDMs). We clarify the model input parameters and derive
the Yukawa couplings considering the two types of CP-violating sources: one
from the Higgs potential and the other from the three complex alignment
parameters $\zeta_{f=u,d,e}$. We consider the theoretical constraints from the
perturbative unitarity and for the Higgs potential to be bounded from below as
well as the experimental ones from electroweak precision observables. Also
considered are the constraints on the alignment parameters from flavor-changing
$\tau$ decays, $Z\to b\bar b$, $\epsilon_K$, and the radiative $b\to s\gamma$
decay. By introducing the basis-independent Yukawa delay factor
$\Delta_{H_1\bar f f}\equiv |\zeta_{f}|(1-g_{_{H_1VV}}^2)^{1/2}$, we scrutinize
the alignment of the Yukawa couplings of the lightest Higgs boson to the SM
fermions.
