  We present the results of our recent analyses of the form factors F_pi(Q^2)
and F_{P gamma}(Q^2), P = pi, eta, eta', within the local-duality version of
QCD sum rules. To probe the expected accuracy of this method, we consider, in
parallel to QCD, a quantum-mechanical potential model. In the latter case, the
exact form factor may be calculated from the solutions of the Schr\"odinger
equation and confronted with the result from the quantum-mechanical
local-duality sum rule. We find that the local-duality sum rule is expected to
yield reliable predictions for both F_pi(Q^2) and F_{pi gamma}(Q^2) in the
region Q^2 > 5-6 GeV^2. Moreover, in this region the accuracy of this approach
improves rather fast with increasing Q^2. For the elastic form factor
F_pi(Q^2), we are therefore forced to conclude that large deviations from the
local-duality limit in the region Q^2 = 20-50 GeV^2 reported in some recent
theoretical studies seem to us unlikely. The data on the eta, eta' to gamma
gamma* transition form factors meet pretty well the predictions of a
"local-duality model." Interestingly, recent results for the pi to gamma gamma*
transition form factor hint at a violation of local duality rising with Q^2;
this is at odds with the eta and eta' cases and all our experience from quantum
mechanics.
