The quantum Hall effect (QHE) is one of the most prominent effects in modern solid state physics. Since its discovery, the effect has been attracting interest by a steadily increasing community of researchers. The research activities have been focussed on both application aspects and the basic physics of the effect. The limits of the QHE, in particular its persistence at higher currents, are of crucial importance for the application of the effect as a resistance standard. The observation of the current-induced breakdown of the QHE initiated a variety of experimental and also theoretical work. In this article, the experiments related to the breakdown of the QHE are reviewed. Some current theories are discussed in conjunction with the experiments. Although no comprehensive theory of the breakdown is available yet, an at least qualitatively conclusive picture can be provided on the basis of the present knowledge.