This article reviews the physics of deep-inelastic lepton-hadron processes in the region of small $x$, where $x$ is the Bjorken scaling variable. The theoretical concepts concerning the Regge limit of deep-inelastic scattering are summarized and recent theoretical results on the small-$x$ limit of parton distributions in perturbative QCD are discussed. Presently available experimental data on the free- and bound-nucleon structure functions at small $x$ are reviewed in detail and their theoretical interpretations (including the low-$x$, low-$Q^2$ region) are discussed. QCD predictions are given for the deep-inelastic scattering structure functions $F_2$ and $F_L$ in the small-$x$ (${10}^{-5\mathrm{}}<x<\mathrm{}{10}^{-2\mathrm{}}$) and moderately large-$Q^2$ region relevant for HERA ($Q^2\sim 10$ Ge${\mathrm{V}}^2$).

DOI:https://doi.org/10.1103/RevModPhys.64.927