We outline a new approach to X-ray projection microscopy in a scanning electron microscope (SEM), which exploits phase contrast to boost the quality and information content of images. These developments have been made possible by the combination of a high-brightness field-emission gun (FEG)-based SEM, direct detection CCD technology and new phase retrieval algorithms. Using this approach we have been able to obtain spatial resolution of < 0.2 µm and have demonstrated novel features such as: (i) phase-contrast enhanced visibility of high spatial frequency image features (e.g. edges and boundaries) over a wide energy range; (ii) energy-resolved imaging to simultaneously produce multiple quasi-monochromatic images using broad-band polychromatic illumination; (iii) easy implementation of microtomography; (iv) rapid and robust phase/amplitude-retrieval algorithms to enable new real-time and quantitative modes of microscopic imaging. These algorithms can also be applied successfully to recover object–plane information from intermediate-field images, unlocking the potentially greater contrast and resolution of the intermediate-field regime. Widespread applications are envisaged for fields such as materials science, biological and biomedical research and microelectronics device inspection. Some illustrative examples are presented. The quantitative methods described here are also very relevant to projection microscopy using other sources of radiation, such as visible light and electrons.