Flavour violating couplings of the 125 GeV Higgs boson are a generic feature in theories with more than one source of electroweak symmetry breaking (for instance general Two Higgs Doublet Models) or theories with higher-dimensional operators in the Higgs/Yukawa sector. In this talk, we explore constraints on such couplings from low-energy experiments as well as detection prospects at the LHC. There, the most promising search channels are h -> mu tau, h -> e tau in the lepton sector and t -> h q in the quark sector. In the latter case, we show that even searches using jet substructure techniques on fully hadronic final states can help to improve the sensitivity. Going one step further, we then discuss the possibility that Higgs couplings violate not only flavour, but also CP, leading for instance to a small difference between BR(h -> e+ mu-) and BR(h -> e- mu+). Finally, we comment on the excess observed recently by CMS in the h -> mu tau final state.
