Spontaneous $CP$ violation in the 2HDM: Physical conditions and the alignment limit

For the general two-Higgs-doublet model, we present conditions for having spontaneous $CP$ violation, in terms of physical masses and couplings. These relations involve the charged Higgs mass, its cubic couplings with neutral scalars and quartic coupling, and become particularly simple in the alignment limit. In the simplified model with softly broken ${\mathcal{Z}}_2$ symmetry, some deviation from alignment is required for spontaneous $CP$ violation to be present.