QCD calculations of heavy quarkonium states

Recent results on the QCD analysis of bound states of heavy (q) over barq q uarks are reviewed, paying attention to what can be derived from the theory with a reasonable degree of rigour. We report a calculation of be bound st ates; a very precise evaluation of b, c quark masses from quarkonium spectr um; the NNLO evaluation of Y --> e(+)e(-); and a discussion of power correc tions. For the b quark pole mass we get, including O(m(c)(2)/m(b)(2)) and O (Phi (5)(s) log alpha (s)) corrections, m(b) = 5.020 +/- 0.058 GeV; and for the MS mass the result, correct to O(alpha (2)(s)), For the decay Y --> e( +)e(-), higher corrections are too large to permit a reliable calculation, but we can predict a toponium width of 13 +/- 1 keV.