Refraction through curved surfaces, reflection from curved mirrors in grazing incidence, and diffraction from Fresnel zone plates are key hard x-ray focusing mechanisms. In this article, we present materials used for refractive x-ray lenses. Important properties of such x-ray lenses include focusing strength, shape, and the material’s homogeneity and absorption coefficient. Both the properties of the initial material and the fabrication process result in a lens with imperfections, which can lead to unwanted wavefront distortions. Different fabrication methods for one-dimensional and two-dimensional focusing lenses are presented, together with the respective benefits and inconveniences that are mostly due to shape fidelity. Different materials and material grades have been investigated in terms of their homogeneity and the absence of inclusions. Single-crystalline materials show high homogeneity, but suffer from unwanted diffracted radiation, which can be avoided using amorphous materials. Finally, we show that shape imperfections can be corrected using a correction lens.