  We study the available data on exclusive leptonic and semileptonic $c\to
s\ell^+\nu$ decays within the Standard Model and beyond. Our analysis accounts
for theory correlations between the relevant hadronic matrix elements through
application of dispersive bounds. We find that, within a global analysis, the
dispersive bounds are generally well respected and only mildly affect the
extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{cs}|$.
Assuming Standard Model dynamics, we obtain $$
  |V_{cs}| = 0.957 \pm 0.003\,, $$ which is compatible with the HFLAV/PDG
reference value $|V_{cs}| = 0.975 \pm 0.006$ at the $2.7\,\sigma$ level. Our
findings lead to significant deficits in the second-row and second-column
unitarity relations of the CKM matrix. Allowing for beyond the SM contributions
in the Weak Effective Theory, we find very strong constraints on potential
(pseudo)scalar and tensor effects. However, the data still permits sizeable
CP-violating right-handed currents.
