One of the high-resolution X-ray microscopy techniques currently being developed at the Swiss Light Source (SLS), as in other places, is based on ptychographic imaging. Ptychography is a coherent diffractive imaging (CDI) technique that bypasses the need for high-numerical-aperture X-ray optics by "phasing" diffraction patterns. Measured in the Fraunhofer far field, the intensity distribution of coherent light scattered by a specimen is easily related to the wave field directly past the specimen by little more than a Fourier transform. However, only intensities are measurable, and the all-important phase information needs to be "retrieved" through analytical means. CDI is insensitive to aberrations and manufacturing limitations of optics and can yield highly resolved images with quantitatively interpretable contrast.