  In many extensions of the Standard Model, the alignment in flavor space of
the fermion mass matrices and the Yukawa coupling matrices can be broken. The
physical scalar boson $h(125)$ could then have flavor changing couplings. In
this talk, we summarize constraints on such couplings from rare decay searches,
and we investigate current and future detection prospects at the LHC. We
emphasize the importance of several yet unexplored final states: (i) anomalous
single top + $h$ production in $p p \to t h$, arising from $tuh$ couplings (but
not from the more widely studied $tch$ couplings); (ii) $p p \to t + (H^0 \to h
h)$ through $tuh$ couplings in the context of a Two Higgs Doublet Model (2HDM),
perhaps the simplest model with flavor violation in the scalar sector; (iii) $p
p \to H^0 \to \tau\mu$ in the 2HDM context. For all of these processes, we
perform a detailed phenomenological studies. Finally, we comment on the
possibility of flavor violation combined with CP violation, which may be
interesting if the current CMS hint for $h \to \tau\mu$ gets corroborated.

High Energy Physics - Phenomenology