For the next generation X-ray astronomy missions two main technological goals have to be achieved: (1) the possibility of making soft X-ray (0.1 - 10 keV) optics with much larger effective areas compared to the missions Chandra and XMM- Newton but still maintaining good angular resolution (better than 15 arcsec); (2) the extension of the use of focusing optics to the hard X-ray energy band (E equals 10 - 100 keV) by means of multilayer coating optics. The Brera Astronomical Observatory (Italy) is currently involved in technological development activities for the achievement of both these objectives. Concerning the realization of large diameter soft X-ray optics with low weight and good imaging capabilities, our efforts are devoted to the development of carriers made of ceramic materials like SiC and Alumina (Al2O3). The low density and the good mechanical parameters of these materials are very promising for this purpose. The technology for manufacturing hard X-ray optics based on multilayer mirrors, will be instead directly derived, with opportune modifications, from the replication process based on Nickel electroforming. This approach was already successfully used for the fabrication of the soft X-ray optics with Au coating of the Beppo-SAX, JET-X, SWIFT and XMM-Newton space experiments. In this case the use of Nickel instead of ceramics for the realization of the mirror carriers remains appropriate, due to the fact that, also for long focal length, hard X-ray telescopes are characterized by small diameters. In this paper we will present the more recent progresses achieved in pursuing these studies.