CP Violation and Mixing in Beauty Sector: A Theoretical Overview

We provide an overview of the latest progress in the study of CP violation and mixing in the $B$ meson decays. Studying the $B^0_d \to J/\psi K^0_S$ and $B^0_s \to J/\psi \phi$ decays, we focus on the determination of the mixing phases $\phi_d$ and $\phi_s$, including hadronic uncertainties with the help of the data. CP violation in the non-leptonic decays $B \to \pi K$ and $B^0_s \to D_s^{\mp} K^{\pm}$ indicate puzzling patterns. Could these puzzles indicate New Physics?