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Domain structure in materials is important for their physical properties, technological uses and response to external perturbations. Domains are small regions within a material with a consistent atomic structure that may have different ordering origins or different orientations. Domain structure is present in any material which exhibits super-structure ordering with correlation lengths shorter than the extent of the sample. The domain size is controlled by the strength of the ordering interactions and growth conditions. Domains are present in a huge range of materials from con¬densed matter to biological samples with a structure unique to the individual sample. For domains in crystalline samples with sizes of Angstroms to nanometres X-rays are an ideal probe. Many domain systems exhibit no X-ray amplitude contrast, i.e. all domains attenuate the X-ray beam uniformly, the domain structure is apparent only in the deviation of the phase of the incident X-ray beam. An imaging method is required which is sensitive to these phase differences. Coherent X-ray Diffraction Imaging (CXDI) is a method which exploits the Fourier transform relationship between the sample and its far field diffraction pattern collected at a pixellated detector to iteratively solve the phase problem and reconstruct an amplitude and phase image of the sample. Support based coherent X-ray diffraction methods have been successfully applied to the three dimensional imaging of crystalline structures by collecting the scattering around the sample Bragg peaks in reflection geometry. In general, phase retrieval algorithm constraints require that the sample is isolated within the X-ray beam and as a result these methods have not been successful at imaging extended domain systems. Ptychography is a combined experimental and analysis procedure that can overcome the requirement for the sample to be isolated by collecting a series of diffraction patterns from overlapping regions of the sample. This thesis develops the ptychography algorithms and experimental methods for use in Bragg geometry with the goal of imaging phase domain structures in extended crystalline samples. Bragg coherent diffraction imaging and ptychography methods are reviewed before the adaptations of the experimental method and algorithm for the application of ptychography in Bragg geometry are discussed and detailed. Simulations of ptychography on phase domain structures and a Bragg geometry ptychography X-ray experiment with a specifically designed phase domain test sample confirm that the method is capable of providing accurate quantitative phase information on the domain structure of extended samples. A coherent diffraction experimental setup for ptychography is developed at Diamond beamline I16. Bragg ptychography is applied to the investigation of domain structure in a niobium thin film and anti-phase domain structure in the binary alloy Fe65Al35 and the results of the reconstructions are presented.