X-ray spectral analysis plays a major role as a diagnostic for hot, dense plasmas. One means for collecting spectra is the use of convex-curved diffraction crystals. Synthetic multilayer structures offer high reflectivity for soft x-rays. Convex diffraction surfaces can be formed by sputtering onto smooth surfaces and by dipping into solutions such as lead myristate. Convex-curved multilayer structures have been evaluated by analytical diffraction models and experimentally by collecting aluminum spectra from plasmas generated by exploded wires sources and by focused laser beams.