Development of single pixel x-ray microcalorimeters at our institutes, employing superconducting-to-normal phase transition thermometers operating at about 100 mK, generally called Transition-Edge-Sensors (TES), has now resulted in an energy resolution of 3.9 eV FWHM for 5.89 keV x-rays in combination with a response time of 100 μs. Pixel arrays of these detectors, presently under development, will allow for unprecedented x-ray spectroscopy of spatially extended cosmic x-ray sources such as clusters of galaxies, supernova remnants, the galactic diffuse x-ray background and the arm-hot intergalactic medium. Optimization of these cryogenic imaging detectors around 1 keV, in combination with large-area x-ray optics, makes them the most suitable sensor for study of the formation and evolution of hot matter in the universe at large redshift. This detector concept is therefore included in the model payload of the XEUS mission, presently under study by ESA and ISAS. Smaller scale low energy x-ray spectroscopy missions could however generate significant progress in the understanding of supernova remnants, cluster of galaxies and galactic and intergalactic diffuse x-ray emission. This paper presents some science cases, which make explicit use of the unique combination of high efficiency, high spectral resolution and imaging of cryogenic x-ray imaging spectrometers. Furthermore it discusses the present development status of these imaging spectrometers at our institutes, their operating principles and expected performance figures.