Several mechanisms can induce a detectable amount of linear polarization (≥l%) in spectral lines emitted by the outer solar atmosphere at EUV/FUV wavelengths (i.e., 100 Å ≤ λ ≤ 1500 Å): (1) Polarization in FUV lines (up to 20%) can be originated by resonance scattering of radiation anisotropically illuminating the emitting atoms. Modifications of this polarization can then result from the presence of a magnetic field (Hanle effect). (2) Impact line polarization can arise from anisotropic collisional excitation ofthe EUV-emitting atoms by particles (electrons, protons) with non-Maxwellian velocity distributions. We suggest how new technological developments in the production of ultrasmooth, low-scatter flow-polished mirror substrates and high-quality multilayer and interference film coatings can make possible some new optical instruments for the observation of these polarization effects. We give the relevant observational parameters for all-reflective FUV/EUV imaging polarimeters. A coronagraph/polarimeter, operating at hydrogen Lyman a, could provide, via the Hanle effect, the first direct measurement of coronal vector magnetic fields. An EUV polarimeter, operating at EUV helium lines (e.g., 304 Å, 584 Å), could observe impact polarization phenomena occurring in solar flares. The reflecting polarization analyzers for these instruments will operate at the Brewster angle and will be coated with thin-film interference coatings or multilayer coatings. We describe several FUV/EUV polarimeter designs based on these polarization optics.