Abstract　 　　  

   The Herschel space mission and the SOFIA airborne telescopes have provided a full access to the submillimeter spectral domain.In this talk I will present advances in the understanding of the diffuse interstellar medium, that were obtained thanks to Herschel and SOFIA. Absorption spectroscopy of hydrides and fine structure lines toward bright background continuum sources have led to a renewed view of the diffuse ISM physical conditions, and to the first step of molecule formation in the ISM. Diagnostics of the m olecular gas, cosmic ray ionization rate, dissipation of turbulence, elemental abundances, established for the local ISM, can now be used in external galaxies up to very distant ones