Supported rhenium oxide has attracted much attention as solid catalyst for the olefin metathesis reaction because of practical applications. These catalysts are composed of rhenium oxide dispersed over a high surface-area support, such as alumina or silica-alumina. They have a high activity and high selectivity at temperatures of 0-100 degrees C, while they bring about the metathesis of functionally substituted olefins when promoted with a suitable organometallic compound. The interaction of rhenium oxide with the support has been studied by a number of characterisation techniques, resulting in a detailed picture of the structure of the supported rhenium oxide. In this paper an overview is given of the current knowledge about rhenium-based metathesis catalysts, in particular the industrially used Re2O7/Al2O3 catalyst.