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 $B_d^0\to J\mathrm{/}\psi K_S^0$ and $B_s^0\to J\mathrm{/}\psi \phi$ 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 $B_s^0\to D_s^{\mp }{K}^{\pm }$ indicate puzzling patterns. Could these puzzles indicate New Physics?