Asymptotic freedom in deep inelastic processes in the leading order and beyond

The present status of quantum chromodynamics formalism for inclusive deep-inelastic scattering is reviewed. Leading-order and higher-order asymptotic freedom corrections are discussed in detail. Both the formal language of operator product expansion and renormalization group and the intuitive parton model picture are used. Systematic comparison of asymptotic freedom predictions with deep-inelastic data is presented. Extensions of asymptotic freedom ideas to other processes such as massive $\ensuremath{\mu}$-pair production, semi-inclusive deep-inelastic scattering, ${e}^{+}{e}^{\ensuremath{-}}$ annihilation, and photon-photon scattering are briefly discussed. The importance of higher-order corrections is emphasized.