  The Two-Higgs Doublet Model (2HDM) is a well-motivated theoretical framework
that provides additional sources of CP Violation (CPV) beyond the Standard
Model (SM). After studying the vacuum topology of a general (convex) 2HDM
potential, we unambiguously identify three origins of CPV: (I) Spontaneous CPV
(SCPV), where the vacuum manifold has at least two degenerate CPV minima
disconnected by domain walls, (ii) Explicit CPV (ECPV) with one single CPV
ground state, and (iii) Mixed Spontaneous and Explicit CPV (MCPV), where the
theory possesses more than one $non$-degenerate CPV local minimum. Most
importantly, we define a novel complex parameter $r_{\rm CP}$ whose norm and
phase control the three different realisations of CPV, at least at the tree
level. In all these scenarios, only two CPV phases can be made independent, as
any third CPV parameter will always be constrained via the CP-odd tadpole
condition. Since ECPV vanishes in 2HDMs where SM Higgs alignment is achieved
naturally through accidental continuous symmetries, we analyse the possibility
of maximising CPV through soft and explicit breaking of these symmetries. We
derive upper limits on key CPV parameters that quantify the degree of SM
misalignment from constraints due to the non-observation of an electron
Electric Dipole Moment (EDM). Finally, we delineate the CP-violating parameter
space of the so-constrained naturally aligned 2HDMs that can further be probed
at the CERN Large Hadron Collider (LHC).
