The principal limitation to the widespread deployment of X-ray phase imaging in a variety of applications is probably versatility. A versatile X-ray phase imaging system must be able to work with polychromatic and non-microfocus sources (for example, those currently used in medical and industrial applications), have physical dimensions sufficiently large to accommodate samples of interest, be insensitive to environmental disturbances (such as vibrations and temperature variations), require only simple system set-up and maintenance, and be able to perform quantitative imaging. The coded-aperture technique, based upon the edge illumination principle, satisfies each of these criteria. To date, we have applied the technique to mammography, materials science, small-animal imaging, non-destructive testing and security. In this paper, we outline the theory of coded-aperture phase imaging and show an example of how the technique may be applied to imaging samples with a practically important scale.