Coherent diffraction imaging(CDI) is a lensless computational imaging technique, which reconstructs the amplitude and phase of an object directly from diffraction intensity measurement by solving the phase problem using iterative algorithms. CDI can provide images at the diffraction limit resolution that is only determined by the wavelength of radiation source and the effective numerical aperture of the recorded data. Since CDI has no need for high quality imaging optics, it is suitable for short wavelength radiations such as deep ultraviolet, X-rays, and electron beam, for which imaging optics of high performance are difficult to make. Meanwhile, the past 20 years have seen rapid progress of new type of light sources (cold emission electron guns, 3rd and 4th generation synchrotron X-rays sources, and free-electron lasers), array detectors with single particle sensitivity and broad dynamic range. All those progresses greatly promote the development of CDI. At present, CDI has shown some unique advantages over traditional methods in some study of materials science and biology, and gradually becomes a mainstream technology for certain applications. This paper briefly summarized the history of CDI with a focus on ptychography and coherent modulation imaging.