  We evaluate the next-to-next-to-leading order corrections to the
hard-scattering amplitude of the photon-to-pion transition form factor. Our
approach is based on the predictive power of the conformal operator product
expansion, which is valid for a vanishing $\beta$-function in the so-called
conformal scheme. The Wilson--coefficients appearing in the non-forward
kinematics are then entirely determined from those of the polarized
deep-inelastic scattering known to next-to-next-to-leading accuracy. We propose
different schemes to include explicitly also the conformal symmetry breaking
term proportional to the $\beta$-function, and discuss numerical predictions
calculated in different kinematical regions. It is demonstrated that the
photon-to-pion transition form factor can provide a fundamental testing ground
for our QCD understanding of exclusive reactions.
