Modeling the local interstellar medium

The state of our observational and theoretical knowledge of the local inter stellar medium (LISM) is reviewed. The LISM stretches out from the local Cl oud, surrounding the solar system to the boundary of the Local Bubble, whic h is a region of distinct anticorrelation between HI (N-H < 10(20) cm(-2)) and 1/4 keV diffuse soft X-rays. After discussing some key observations in soft X-rays, obtained by ROSAT and DXS, and in the EUV by the EUVE satellit e and the EURD instrument onboard Minisat, I will critically review models of the LISM. Since we cannot determine the plasma state (temperature, densi ty, etc.) directly, the best plasma diagnostic tool is high resolution spec troscopy. The interpretation of the data then has to rely heavily on plasma emission models. I will point out several caveats in the standard procedur e. Preference is given to dynamical models of the Local Bubble in general a nd to non-equilibrium plasma emission models in particular, which have to b e calculated self-consistently. Such a model can explain (i) the deficiency of EUV lines as observed by EUVE, (ii) the dispersion measure and scintill ation properties of a nearby pulsar, (iii) the existence of local neutral H I clouds, and (iv) OVI absorption line widths. New model spectra of the LIS M will be presented and briefly compared with DXS, EUVE and preliminary EUR D results.