  We review the determination of the QED coupling at the Z pole, which is a
crucial parameter for electroweak theory. We include recent e+e- -> hadron data
from Novosibirsk and Beijing to re-evaluate alpha (M_Z^2). We find 1/alpha
(M_Z^2) = 128.973 +/- 0.035 or 128.934 +/- 0.040 according, respectively, to
whether inclusive or exclusive e+e- -> hadron data are used in the interval 1.4
< \sqrt{s} < 2.1 GeV. The error is mainly due to uncertainties in the data in
the low energy region, \sqrt{s} < 2.5 GeV. We find that no advantage is
obtained by analytic continuation of the dispersion relation into the complex s
plane. We show that the hints of structure for \sqrt{s} ~ 2.5 GeV may be
evidence of a non-perturbative gluonic contribution to R(s).
