We provide an analysis of contemporary multilayer optics for extreme ultraviolet (EUV) solar astronomy in the wavelength ranges: λ=12.9-13.3 nm, λ=17-21 nm, λ=28-33 nm, and λ=58.4 nm. We found new material pairs, which will make new spaceborne experiments possible due to the high reflection efficiencies, spectral resolution, and long-term stabilities of the proposed multilayer coatings. In the spectral range λ=13 nm, Mo/Be multilayer mirrors were shown to demonstrate a better ratio of reflection efficiency and spectral resolution compared with the commonly used Mo/Si. In the spectral range λ=17-21 nm, a new multilayer structure Al/Si was proposed, which had higher spectral resolution along with comparable reflection efficiency compared with the commonly used Al/Zr multilayer structures. In the spectral range λ=30 nm, the Si/B4C/Mg/Cr multilayer structure turned out to best obey reflection efficiency and long-term stability. The B4C and Cr layers prevented mutual diffusion of the Si and Mg layers. For the spectral range λ=58 nm, a new multilayer Mo/Mg-based structure was developed; its reflection efficiency and long-term stability have been analyzed. We also investigated intrinsic stresses inherent for most of the multilayer structures and proposed possibilities for stress elimination.