Periodic multilayers are well known as Bragg reflectors for X- rays. A high reflectivity and a wide reflection width are their outstanding features. However, if multilayers shall be used as reflective coating for X-ray optics, especially for wide acceptance angles, uniform layer thicknesses cause chromatic aberrations. These aberrations can be overcome by laterally graded multilayer optics. Their Bragg angle is matched laterally to the incidence angle so that for all points on the reflector, Bragg reflection is obtained for the same wavelength. Three major types of laterally graded multilayer mirrors ('Gobel Mirrors') are applied in X-ray diffractometry: (1) parabolic, (2) elliptic and (3) planar. In this paper, we give design criteria and formulae for these mirrors. Furthermore, we discuss the requirements on the dimensions and the fabrication process. Two different processes suitable for the fabrication, sputter coating and pulsed laser deposition (PLD), are described. The X-ray optical parameters and their characterization are presented for various mirrors designed for Cu K(alpha) , Mo K(alpha) and Cr K(alpha) radiation. From Ni/C and Ni/B4C multilayers, high-photon-flux monochromators with a Cu K(beta) /K(alpha) intensity ratio of about 1:1000 have been realized. The divergence of the 'parallel' beam reflected from parabolic mirrors is about 0.02 degrees, which is one order of magnitude lower than the divergence of polycapillary optics, monocapillary optics and waveguides. Comparing the photon flux density in a high resolution diffraction setup with and without mirror optics a gain factor of 16 was achieved for parabolic Ni/B4C multilayer mirrors.