Abstract: In computer tomography (CT), when an acoustic or electromagnetic wave of finite wavelength is used instead of X-ray to illuminate the object, the Fourier slice theorem should be replaced by the Fourier diffraction theorem, leading to diffraction tomography. This article presents a review of the recent development of diffraction tomography, especially acoustic tomography. Issues discussed include algorithms of non-uniform Fourier transform and its fast implementation, image reconstruction based on intensity measurements only without using phase information, multiple frequency incidence, image reconstruction from incomplete projection data, etc. Applications of diffraction CT in several areas are briefly introduced.