This paper discusses resolution limits for electron-beam fabrication. Electron beams have been used to produce structures 1 nm in size and useful devices with minimum features of about 20 nm. In all cases the resolution is set primarily by the range of the electron interaction phenomena that form the structures, and not by the size of the electron beam used to write the patterns. The beam can be as small as 0.5 nm. All useful devices built to date have been fabricated with conventional resist processes; these have an ultimate resolution of about 10 nm. Experimental data for PMMA, the highest-resolution electron resist, show that resolution is independent of molecular weight and is therefore not a function of the molecular size. The most promising of the methods offering resolution below 10 nm is the direct sublimation of materials such as AlF3 and Al2O3; 1-nm structures have been fabricated, but it has not been possible to convert the structures into useful devices. In addition to the processes which use intermediate patterned layers, there is the possibility of making devices by direct modification of the electrical properties of conductors, semiconductors, or superconductors by means of high-energy electron bombardment. In these cases no intermediate fabrication process would be used, and it might be possible to reach dimensions comparable to the beam diameter.