[en] The technical and financial limitations to the energy that can be obtained from conventional synchrotrons and linacs by increasing their size is discussed. It is generally assumed that existing ideas will not be adequate for 'accelerators for the 21st century', except perhaps for the first decade or so. Alternative approaches ar then discussed, and four methods that have been suggested for using lasers are outlined. These are characterized by the terms inverse Cherenkov, grating, inverse free electron laser, and beat wave. All have attractive features, but there are severe limitations also. Attempts to estimate cost and power requirements can hardly yet be made. (author)