Studies of the CKM matrix elements and $b$-hadron production using semileptonic decays at LHCb

Exclusive semileptonic $b$-hadron decays are under good theoretical control, which allows precise determinations of the CKM matrix elements, $V_{ub}$ and $V_{cb}$. The large production of $\Lambda_b$ baryons and $B_s$ mesons at the LHC allows LHCb to provide complementary information with respect to the B-factories in this sector, as well as in the measurement of the shape of the $\Lambda_b$ differential decay rates. Novel experimental techniques are used to measure the fraction of semileptonic $B^+$ to charm meson decays, in order to improve the understanding of the inclusive charm semileptonic rate and the background description for analyses exploiting exclusive $b\rightarrow c$ and $b\rightarrow u$ transitions. The latest LHCb results on CKM matrix element determination and related measurements and searches are presented.