Since in 1948 X-rays were detected from the solar corona, stellar coronae were among the first predicted non-solar X-ray sources. However, because of their relatively low X-ray luminosity, the first non-solar stellar corona was not detected in X-rays until 1974 - twelve years after the discovery of the first non-solar X-ray source. After the 1980s, with the advent of sensitive X-ray imaging instruments on board the EINSTEIN, EXOSAT, and later the ROSAT observatories, the study of stellar coronae has become a vastly growing field of research. These X-ray observations have demonstrated that X-ray emitting coronae are a common feature among stars on the cool side of the Hertzsprung-Russell diagram, with the probable exception of single very cool giant and supergiant stars and A-type dwarfs. The instruments on board these satellites provided for the first time a taste of what can be achieved with X-ray spectroscopy and with the advent of the EUVE (1992) and ASCA (1993), detailed spectroscopy of stellar coronae in the EUV and X-ray regimes got off to a real start. The observations have permitted the identification of coronal material at different temperatures whose existence relates to a range of possible magnetic loop structures in the hot outer atmospheres of stars. The higher spectral resolution of the next generation of spectrometers on board NASA's AXAF (1998), ESA's XMM (1999), and the Japanese ASTRO-E (2000) will improve the determination of coronal temperature structure, abundances, and densities from which loop geometries can be derived and will enable velocity diagnostics. This paper reviews our present knowledge of observational stellar X-ray spectroscopy up to EUVE and ASCA and briefly discusses the perspectives for coronal diagnostics offered by AXAF, XMM, and ASTRO-E.