Measurements of CP violation in B mixing through $B \to J/\psi X$ decays at LHCb

B mesons provide an ideal laboratory for measurements of CP violation and searches for CP violation beyond the Standard Model. Recent measurements of the mixing phases of the $B_s^0$ and $B^0$ mesons, $\phi_s$ and $\sin2\beta$, using decays to $J/\psi X$ final states are presented. In view of future improved measurements, a good understanding of pollution from sub-leading penguin topologies in these decays is needed. Those can be probed using suppressed decays like $B_s^0 \to J/\psi K_S^0$ and $B_s^0 \to J/\psi \overline{K}^{*0}$. Recent results using these decay modes are presented.