A scanning soft x-ray microscope has been built and operated at the National Synchrotron Light Source. It makes use of a mini-undulator as a bright source of 3.2-nm photons. An electron beam fabricated Fresnel zone plate focuses the beam onto the specimen, which is scanned under computer control. The scanning stage can be moved by both piezoelectric transducers and stepping motors, and the location is monitored by a high-speed laser interferometer. X rays transmitted through the specimen are detected using a flow proportional counter. Images of biological specimens and of artificial microstructures have been made with resolution in the 75-100-nm range. Acquisition time for 256×256-pixel images is about 5 min.