The computational methods and applications of diffractive diffractive imaging (lensless) lensless imagingimaginglensless imaging are reviewed. Far-field scattering (e.g., by neutrons, electrons, light, or x-rays) by a nonperiodic localized potential is detected and the phase problem solved using iterative optimization methods, which allows a three-dimensional image of the object potential to be reconstructed without the need for a lens. The history of the subject and its relationship to the crystallographic phase problem are reviewed, together with a summary of theory, algorithms, uniqueness issues, resolution limits, the constraint ratio concept, and coherence requirements. Applications, from various forms of microscopy (electron, optical, and x-ray) to snapshot x-ray laser single-particle imaging, are reviewed. The method of ptychography, which achieves a similar aim, is reviewed elsewhere in these volumes.