Disagreements between experimental results and Standard Model theoretical predictions found in B meson decays, initiated many theoretical studies in flavour physics. The anomalous behaviour observed in B meson decays are known as $R_{D^{(∗)}}$ and $R_{K^{(∗)}}$ puzzles. The first one refers to the deviations in the decays in the ratio of the decay widths for $B \rightarrow D^{(∗)}τν$ and $B\rightarrow D^{(∗)}μν$, while the second one is related to the ratio of the decay widths for $B\rightarrow K^{(∗)}$$μ^+μ^−$ and $B\rightarrow K^{(∗)}$$e^+e^−$ transition. In addition, the measured muon anomalous magnetic moment differs from the SM pre- dictions. I briefly review main results coming from the SM studies and the effective Lagrangian approach containing New Physics for $R_{D^{(∗)}}$ and $R_{K^{(∗)}}$.Then I discuss basic features of leptoquark models which can resolve both B meson anomalies. If New Physics is confirmed in B decays a number of processes at low and high energies should confirm its presence.