CP violation in the Higgs couplings to fermions is an intriguing, but not yet extensively explored possibility. We use inclusive and differential LHC Higgs boson measurements to fit the CP structure of the Higgs Yukawa couplings. Starting with simple effective models featuring CP violation in a single Higgs–fermion coupling, we probe well-motivated models with up to nine free parameters. We also investigate the complementarity of LHC constraints with the electron electric dipole moment bound, taking into account the possibility of a modified electron Yukawa coupling, and assess to which extent CP violation in the Higgs–fermion couplings can contribute to the observed baryon asymmetry of the universe. Even after including the recent analysis of angular correlations in H→ τ+τ- decays, we find that a complex tau Yukawa coupling alone may be able to account for the observed baryon asymmetry, but with large uncertainties in the baryogenesis calculation. A combination of complex top and bottom quark Yukawa couplings yields a result four times larger than the sum of their separate contributions, but remains insufficient to account for the observed baryon asymmetry. © 2022, The Author(s).