We investigate the CP structure of the Higgs couplings to fermions and gluons by using constraints from LHC measurements and the electric dipole moment of the electron. We further use these constraints to assess how much of the observed baryon asymmetry of the universe can be explained by CP violation in the Higgs sector. Additionally, our expected limits on the CP phase of the top-Yukawa coupling from both a global fit and a multivariate approach are stronger than currently existing measurements.