  Two of the elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix,
$|V_{ub}|$ and $|V_{cb}|$, are extracted from semileptonic B decays. The
results of the B factories, analysed in the light of the most recent
theoretical calculations, remain puzzling, because for both $|V_{ub}|$ and
$|V_{cb}|$ the exclusive and inclusive determinations are in clear tension.
Further, measurements in the $\tau$ channels at Belle, Babar, and LHCb show
discrepancies with the Standard Model predictions, pointing to a possible
violation of lepton flavor universality. LHCb and Belle II have the potential
to resolve these issues in the next few years. This article summarizes the
discussions and results obtained at the MITP workshop held on April 9--13,
2018, in Mainz, Germany, with the goal to develop a medium-term strategy of
analyses and calculations aimed at solving the puzzles. Lattice and continuum
theorists working together with experimentalists have discussed how to reshape
the semileptonic analyses in view of the much higher luminosity expected at
Belle II, searching for ways to systematically validate the theoretical
predictions in both exclusive and inclusive B decays, and to exploit the rich
possibilities at LHCb.
