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 → Dτν 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

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... this mode using τ decays to hadronic final states, which is essentially independent of previous measurements from Belle. With this method, the τ lepton polarization in B → Dτν has been measured for the first time. Recent results on purely leptonic decay, B → µν will also be discussed. The analyses are based on the full data set of Belle containing 772 million BB pairs.