  The `renormalon' or `dispersive' method for estimating non-perturbative
corrections to QCD observables is reviewed. The corrections are
power-suppressed, i.e. of the form $A/Q^p$ where $Q$ is the hard process
momentum scale. The renormalon method exploits the connection between
divergences of the QCD perturbation series and low-momentum dynamics to predict
the power, $p$. The further assumption of an approximately universal low-energy
effective strong coupling leads to relationships between the coefficients $A$
for different observables. Results on $1/Q^2$ corrections to deep inelastic
structure functions and $1/Q$ corrections to event shapes are presented and
compared with experiment. Shape variables that could be free of $1/Q$ and
$\as(Q^2)/Q$ corrections are suggested.
