Theory of CP violation in B decays

The study of CP violation in $B$-meson decays has already reached a high level of precision, which will be pushed even higher in the future era of Belle-II and the LHCb upgrade. %Important probes of CP violation are the $B_d^0$ and $B_s^0$ mixing phases and the CKM angle $\gamma$. Here, the theoretical challenge is to control the uncertainties from strong interactions to distinguish between the Standard Model and possible New Physics effects. In this talk, I will present a selected overview of recent theoretical developments in this field. This includes, in particular, the semileptonic asymmetry $a_{\text{sl}}^s$ and extractions of the CKM angle $\gamma$ and the $B_d^0$ and $B_s^0$ mixing phases. I focus on recently proposed strategies in which the theory uncertainties can be controlled through data using flavour symmetries of the strong interaction. A newly found puzzle in the $B\to \pi K$ system is highlighted and a theoretically clean way to determine the underlying electroweak penguin parameters is discussed. Finally, the recent progress to describe three-body $B$ decays in QCD factorization is discussed.