X-ray free-electron lasers (XFELs) are currently under development and will provide a peak brightness more than 10 orders of magnitude higher than modern synchrotrons. The goal of this project was to perform the fundamental research to evaluate the possibility of harnessing these unique x-ray sources to image single biological particles and molecules at atomic resolution. Using a combination of computational modeling and experimental verification where possible, they showed that it should indeed be possible to record coherent scattering patterns from single molecules with pulses that are shorter than the timescales for the degradation of the structure due to the interaction with those pulses. They used these models to determine the effectiveness of strategies to allow imaging using longer XFEL pulses and to design validation experiments to be carried out at interim ultrafast sources. They also developed and demonstrated methods to recover three-dimensional (3D) images from coherent diffraction patterns, similar to those expected from XFELs. The images of micron-sized test objects are the highest-resolution 3D images of any noncrystalline material ever formed with x-rays. The project resulted in 14 publications in peer-reviewed journals and four records of invention.