  We present a pedagogical review of the universal scaling properties displayed
by the structure function F_2 at small x and large Q^2 as measured at HERA. We
first describe the derivation of the double asymptotic scaling of F_2 from the
leading-order Altarelli-Parisi equations of perturbative QCD. Universal
next-to-leading order corrections to scaling are also derived. We explain why
the universal scaling behaviour is spoiled when the initial distributions rise
too steeply by considering the nonsinglet distribution F_2^p-F_2^n as an
explicit example. We then examine the stability of double scaling to the
inclusion of higher order singularities, explaining how the perturbative
expansion at small x can be reorganized in such a way that each order is given
by the sum of a convergent series of contributions which are of arbitrarily
high order in the coupling. The wave-like nature of perturbative evolution is
then shown to persist throughout almost all the small x region, giving rise
asymptotically to double scaling for a wide class of boundary conditions.
