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With the aim of concentrating hard X- and γ-rays coming from celestial sources in the 100–1000 keV energy range, the concept of Laue lens was introduced more than 50 years ago. Crystals are the core of a Laue lens, since they focus the incoming X-rays through Bragg diffraction. For concrete applications, crystals characterized by high diffraction reflectivity are needed along with high-resolution focusing of diffracted photons. Here, an extensive comparison of the types of crystals proposed so far is presented. In order to quantify the focusing capability of a Laue lens based on these crystals, a simulation of a single-ring Laue lens based on the considered optical elements is presented. Finally, the breakthrough in the panorama of diffracting crystals is discussed

Laue lens for astrophysics: Extensive comparison between mosaic, curved, and quasi-mosaic crystals