Measurements of B -> D(*) tau nu at Belle

B -> D(*) tau nu is one of the semileptonic B decays with a feature that a tau lepton exists in the final state. It is sensitive to new physics (NP) preferentially coupling to a tau lepton. The NP may modify branching fractions and decay kinematics of B -> D(*) tau nu. Experimental studies of the ratio of the branching fractions R(D(*)) = BF(B -> D(*) tau nu) / BF(B -> D(*) l nu) (where l = e or mu) show about 4 sigma deviation from the predictions based on the Standard Model. Belle has accumulated the data sample containing 772M BB pairs during operation from 1999 to 2010. Using the full data sample, we have performed three independent measurements. In this seminar, I will focus on the latest analysis using hadronic tau decays tau -> pi nu and rho nu. In addition to a new R(D*) measurement independent of the previous two results, we have succeeded in measuring polarization of the tau lepton in the decay B -> D* tau nu (P_tau(D*)) for the first time by using the feature of two-body tau decays. Based on these results, current constraints on some of the NP models will be presented, including comparison with other measurements such as direct searches. Finally, prospects of the B -> D(*) tau nu studies at Belle II will be discussed.