We have launched a project to promote grating-based X-ray phase imaging/tomography extensively. Here, two main activities are presented for enabling dynamic, or four-dimensional, X-ray phase tomography and nanoscopic X-ray phase tomography by grating interferometry. For the former, while some demonstrations in this direction were performed with white synchrotron radiation, improvement in image quality by spectrum tuning is described. A preliminary result by a total reflection mirror is presented, and as a next step, preparation of a 10% bandpass filter by a multilayer mirror is reported. For the latter, X-ray microscopes available both at synchrotron radiation facilities and laboratories equipped with a Fresnel zone plate are combined with grating interferometry. Here, a preliminary result with a combination of a Lau interferometer and a laboratory-based X-ray microscope is presented.