We present a comprehensive account of a relativistic quark model on the light front which gives the form factors of weak hadronic currents among heavy pseudoscalar and vector mesons in the complete kinematic region 0 <= q2 <= q2max. For the numerical investigations of the B -> D*lνl, B -> πlνl, D -> K*lνl and D -> πlνl semileptonic decays equal time wave functions using the updates values of the ISGW model are adopted. From the available experimental information on branching fractions BR(B -> D* lνl) and BR(B -> πlνl) the CKM parameters Vcb and Vub are estimated to be Vcb = 0.036 +/- 0.002, Vub = 0.0033 +/- 0.0005. It is show that the q2 distribution for the decay B -> D* lνl will allow for an accurate test of the value of Vcb. The model is compared to the experimental data, QCD sum rules and lattice calculations.