We describe several spectroscopic techniques for space-resolved diagnostics of inhomogeneous plasmas from the line and continuous XUV spectra of multiply charged ions, involving measurements of temperature, density, ion composition, ablation velocity, etc. To this end, we have developed a family of stigmatic high-throughput spectroscopic instruments ranging in resolution from 500 to over 20000. The new instruments harness separation of the focusing and dispersion functions: the XUV radiation is dispersed by plane grazing-incidence gratings or transmission diffraction gratings while the focusing is transferred to concave normal-incidence multilayer mirrors or grazing-incidence toroidal mirrors. We have obtained medium-to-high resolution spectra of laser-produced plasmas to infer the plasma parameters (density profiles, expansion velocity, etc). The operating range of a spectrograph which incorporates periodic multilayer mirrors is confined to the resonance reflection band of the mirrors. To meet the demand for broadband stigmatic instruments, a panoramic (110 - 300 angstrom) medium-resolution spectrograph was made employing a Mo/Si multilayer mirror with a lateral gradient of the period structure (0.9 Angstrom/mm) and a transmission diffraction grating (5000 lines/mm). An alternative way to obtain panoramic stigmatic spectra involves the development of broadband aperiodic multilayer mirrors. We have developed a numerical technique based on the fast calculation of derivatives, which allows us to determine aperiodic structures with prescribed reflectance spectra and augmented integral reflectivity. This technique has proved to be efficient both in the soft and hard X-ray ranges.