Inclusive B→ X_c ℓν̅_ℓ and B→ X_u ℓν̅_ℓ decays: current status and future prospects

The inclusive semileptonic B→ X_c ℓν̅_ℓ and B→ X_u ℓν̅_ℓ decays allow for the extraction of the CKM elements |V_cb| and |V_ub| , respectively. These extractions are based on the Heavy-Quark Expansion, where recent progress on both the experimental and theoretical side allow for impressively precise results. We review the recent developments in the study of inclusive decays and give an outlook for the future.