The fact that radiation damage would limit the usefulness of electron microscopy with biological specimens was a concern in the earliest days of the field. Good estimates of what that limitation must be can be made by using Rose's empirical relationship between the inherent image contrast, the exposure used to record an image, and the smallest feature size that is detectable. Such estimates show that it is necessary to average many images in order to obtain statistically well-defined data at high resolution. Structures are now routinely obtained by averaging large numbers of shot-noise limited images, and some of these extend to atomic resolution. The signal level in current images is nevertheless far below what physics would allow it to be. A possible explanation is that beam-induced movement limits the quality of images recorded by electron microscopy. For specimens embedded in vitreous ice, beam-induced movement can even be severe enough to limit the resolution achieved during tomographic reconstruction. The fact that very high-quality images can nevertheless be obtained, although only unpredictably, suggests that it may be possible to devise new techniques of specimen preparation and/or data collection that at least partially overcome beam-induced movement. If so, the need for image averaging would be correspondingly reduced. Published by Elsevier Inc.