In order to preserve the conditions for an environmentally safe machine, at present the selection of materials for the structural components of fusion reactors is made not only on the basis of adequate mechanical properties, behaviour under irradiation, and compatibility with other materials and cooling media, but also on their radiological properties, i.e. radioactivity, decay heat and radiotoxicity. These conditions strongly limit the number of suitable materials to a few families of alloys, generically known as low activation materials. The criteria for making decisions about such materials, the alloys resulting from the application of these ideas and the main issues and problems with their use in a fusion environment are discussed.