A large body of spectral information on X-ray sources has now become available, but the interpretation remains ambiguous. If temperature variations and finite optical depth effects are taken into account, almost any spectrum can be fitted to a model of thermal bremsstrahlung. If a suitable energy spectrum is adopted for the relativistic electrons, a wide variety of synchrotron spectra becomes possible. Although one or the other interpretation may seem artificial in some cases, it nevertheless should be pointed out that a strictly isothermal source would be a miracle and that power-law type energy spectra of the relativistic particles can apply over only a limited range of energies. More satisfactory progress can be made when the spectral data are augmented with structural information, when emission lines can be studied and polarization can be measured. Not only do the intensities of emission lines give much more detailed information on the temperature and density in a hot gas than can be derived from the continuum, but at sufficient resolution velocity fields can also be studied. Useful structural information probably can be obtained only if spatial resolution of 1 arc-min or better is achieved. But one has only to look at the situation in radio astronomy to see how essential this information is for the building of quantitative models.