X-ray imaging of biological samples is progressing rapidly. In this paper we review the progress to date in high-resolution imaging of cellular architecture. In particular we survey the progress in soft X-ray tomography and argue that the field is coming of age and that important biological insights are starting to emerge. We then review the new ideas based on coherent diffraction. These methods are at a much earlier stage of development but, as they eliminate the need for X-ray optics, have the capacity to provide substantially better spatial resolution than zone plate-based methods.