Mixing and $CP$ violation results in $b$-hadron decays at LHCb

Measurements of mixing and $CP$ violation in $b$-hadron decays are great probes to search for physics beyond the Standard Model. A selection of recent results based upon $3.0\ \mathrm{fb}^{-1}$ of LHCb data are presented. These are the first measurement of the $CP$ violating phase $\phi_{s}$ using $B_{s}^{0}\to J/\psi K^{+}K^{-}$ in the mass region above the $\phi(1020)$ resonance and $B_{s}^{0}\to \psi(2S) \phi$ decays, the determination of $B_{s}^{0}$ lifetime using $B_{s}^{0}\to D^{(*)-}\mu^{+}\nu_{\mu}$ decays, the updated measurements of the CKM angle $\gamma$ with $B^{\pm}\to D K^{*\pm}$ and $B_{s}^{0} \to D_{s}^{\mp}K^{\pm}$ decay modes and the CP violation searches in $\varLambda^{0}_{b}\to p\pi^{-}\pi^{+}\pi^{-}$ and $\varLambda^{0}_{b}\to pK^{-}\mu^{+}\mu^{-}$ decays.