Abstract: To meet the requirements of the International X-ray Observatory (IXO), a new kind of diffraction grating called the soft X-ray freestanding blazed transmission grating, or critical-angle transmission (CAT) grating, has been developed by the Massachusetts Institute of Technology team.The CAT grating has the advantages of both transmission and reflection gratings, while avoiding their disadvantages. Its basic concept, principle, and fabrication process are reviewed. Recent advances in this field are also presented.