The calculation of glueball masses based on Maldacena's duality between supergravity and Yang-Mills theory is reviewed. Earlier work for the spin zero sector is extended to the full JPC multiplet for both QCD3 and QCD4. Contrary to expectation, the mass of the 0^++ state associated with the graviton is smaller than the mass of the ~0^++ state from the dilaton. The strong coupling results for IIA supergravity, when restricted to the QCD4 superselection sector, compare remarkably well with the ”known” glueball spectrum of lattice QCD simulations.