An attempt at refraction-based 2D, 2.5D and 3D X-ray imaging of articular cartilage and breast carcinoma is reported. We are developing very high contrast X-ray 2D imaging with XDFI (X-ray dark-field imaging), X-ray CT whose data are acquired by DEI (diffraction-enhanced imaging) and tomosynthesis due to refraction contrast. 2D and 2.5D images were taken with nuclear plates or with X-ray films. Microcalcification of breast cancer and articular cartilage are clearly visible. 3D data were taken with an X-ray sensitive CCD camera. The 3D image was successfully reconstructed by the use of an algorithm newly made by our group. This shows a distinctive internal structure of a ductus lactiferi (milk duct) that contains inner wall, intraductal carcinoma and multifocal calcification in the necrotic core of the continuous DCIS (ductal carcinoma in situ). Furthermore consideration of clinical applications of these contrasts made us to try tomosynthesis. This attempt was satisfactory from the view point of articular cartilage image quality and the skin radiation dose.