Because of the strong absorption of extreme ultraviolet radiation by h
ydrogen and helium, almost every observation with the Extreme Ultravio
let Explorer (EUVE) satellite is affected by the diffuse clouds of neu
tral gas in the local interstellar medium (LISM). This paper reviews s
ome of the highlights of the EUVE results on the distribution and phys
ical state of the LISM and the implications of these results with resp
ect to the interface of the LISM and the heliosphere. The distribution
of sources found with the EUVE all-sky surveys shows an enhancement i
n absorption toward the galactic center. Individual spectra toward nea
rby continuum sources provide evidence of a greater ionization of heli
um than hydrogen in the Local Cloud with an mean ratio of H I/He I of
14.7. The spectral distribution of the EUV stellar radiation field has
been measured, which provides a lower limit to local H II and He II d
ensities, but this radiation field alone cannot explain the local heli
um ionization. A combination of EUVE measurements of H I, He I, and He
II columns plus the measurement of the local He I density with interp
lanetary probes can place constraints on the local values of the H I d
ensity outside the heliosphere to lie between 0.15 and 0.34 cm(-3) whi
le the H II density ranges between 0.0 and 0.14 cm(-3). The thermal pr
essure (P/k = nT) of the Local Cloud is derived to be between 1700 and
2300 cm(-3) K, a factor of 2 to 3 above previous estimates.