  A survey is given of recent developments on the resummed small-$x$ evolution,
in a framework based on the renormalization group equation, of non--singlet and
singlet structure functions in both unpolarized and polarized deep--inelastic
scattering. The available resummed anomalous dimensions are discussed for all
these cases, and the most important analytic and numerical results are
compiled. The quantitative effects of these small-$x$ resummations on the
evolution of the various parton densities and structure functions are
presented, and their present uncertainties are investigated. An application to
QED radiative corrections is given.
