Semileptonic and leptonic $B$ decays are powerful probes to search for physics beyond the Standard Model (SM) as they can be calculated in the SM with high precision. We report recent results on rare $B$ decays with leptons from the Belle experiment at the KEKB $e^+e^−$ collider. The $B\to D^∗\tau\nu$ mode is sensitive to New Physics effects such as a charged Higgs or leptoquark current, while the world average of the branching ratio shows a discrepancy from the SM. Recently, Belle has performed a measurement of this mode using $\tau$ decays to hadronic final states, which is essentially independent of previous measurements from Belle. With this method, the $\tau$ lepton polarization in $B\to D^∗\tau\nu$ has been measured for the first time. Recent results on purely leptonic decay, $B\to\mu\nu$ will also be discussed. The analyses are based on the full data set of Belle containing 772 million $B\bar{B}$ pairs.