Among the methods to focus photons the diffraction in crystals results as one of the most effective for high energy photons. An assembling of properly oriented crystals can form a lens able to focus x-rays at high energy via Laue diffraction in transmission geometry; this is a Laue lens. The x-ray diffraction theory provides that the maximum diffraction efficiency is achieved in ideal mosaic crystals, but real mosaic crystals show diffraction efficiencies several times lower than the ideal case due to technological problems. An alternative and convenient approach is the use of curved crystals. We have recently optimized an efficient method based on the surface damage of crystals to produce self-standing uniformly curved Si, GaAs and Ge tiles of thickness up to 2-3 mm and curvature radii R down to a few meters. We show that, for curved diffracting planes, such crystals have a diffraction efficiency nearly forty times higher than the diffraction efficiency of perfect similar flat crystals, thus very close to that of ideal mosaic crystals. Moreover, in an alternative configuration where the diffracting planes are perpendicular to the curved ones, a focusing effect occurs and will be shown. These results were obtained for several energies between 17 and 120 keV with lab sources or at high energy facilities such as LARIX at Ferrara (Italy), ESRF at Grenoble (France), and ANKA at Karlsruhe (Germany).