Abstract: B meson decays are important players in the search for physics beyond
the Standard Model (SM) of particle physics. Linked to the antimatter-matter asymmetry in the universe, a key interest in this is also improving the understanding of the mechanism of CP violation within the SM. The large amount of data gathered by the B factories and LHCb allows testing the SM with an unprecedented precision, probing scales much higher than the reach of direct searches at the LHC. Naturally, this also requires precise theoretical predictions. In this talk, I will present some of the challenges and new ideas to push the theoretical precision up. Specifically, I will focus on the determination of the CKM element Vcb and QED effects in non-leptonic decays.