The phenomenon of harmonic generation by electrons oscillating in high-intensity laser fields is surveyed and assessed as a means of producing short-wavelength radiation. Starting from the seminal early work by Sarachik and Schappert (1970), simple motivatory examples are given of incoherent harmonic generation via nonlinear scattering from single electrons. More recent studies aimed at observing the coherent version of this effect in underdense plasmas are then reviewed and some problems noted in distinguishing these harmonics from those produced via the analogous nonlinear mechanism from bound electrons in rare gases. Finally, the revival of interest in harmonics reflected from overdense plasmas is considered. Short-pulse laser-generated "surface" harmonics appear to offer a very promising, compact, and efficient means of upshifting coherent radiation to sub-10-nm wavelengths.