Plastic buckling theory is presented, starting with the general theory of uniqueness and bifurcation for elastic-plastic solids. Also asymptotic procedures for estimating the initial post-bifurcation behaviour and the imperfection-sensitivity are presented, based on the classical elastic-plastic solid. The effect of other elastic-plastic constitutive descriptions on bifurcation and post-bifurcation behaviour is discussed. Several numerical analyses of the plastic buckling of plate — or shell structures are reviewed, and special attention is given to the localization of buckling patterns that often occurs as a secondary bifurcation. Finally, the effect of material strain-rate sensitivity on the prediction of plastic instabilities is discussed in some detail.