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, $Z\to b\overline{b}$, ${\epsilon }_K$, and the radiative $b\to s\gamma$ decay. By introducing the basis-independent Yukawa delay factor ${\Delta }_{H^{}\overline{f}f}\equiv \left|{\zeta }_f\right|(1-g_{H^{}VV}^2{)}^{1/2}$, we scrutinize the alignment of the Yukawa couplings of the lightest Higgs boson to the SM fermions.