We are currently studying the semileptonic form factors of mesons with one heavy and one light quark. An accurate calculation of these form factors would provide important new information regarding the Standard Model of High Energy Physics. For example, the decays B -> rho + leptons and B -> pi + leptons determine the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vub. Lack of knowledge of strong interaction effects makes this parameter one of the most poorly determined in the Standard Model with uncertainties of about a factor of two. Further, knowledge of the form factor for B -> K* + gamma, recently observed at CLEO, would make possible a sensitive test of the Standard Model, since this decay is known to be roughly independent of the CKM angles. It is of particular interest as a possible indicator of physics beyond the Standard Model. Finally, the CKM matrix element Vcb is determined from the decay B -> D + leptons and B -> D*+leptons. Because two heavy quarks are involved, the Isgur-Wise heavy quark effective theory (HQET) is typically used to parameterize the decay amplitude as a function of the invariant mass of the leptons. The present lack of knowledge of strong interaction effects in this process is responsible for a 5%--10% uncertainty in the determination of this key matrix element. A systematic and controlled lattice computation of these effects can lead to a significant reduction in the uncertainty. Preliminary results can be found here.