High resolution X-ray spectroscopy of astrophysical sources: current and future

High resolution spectroscopy of cosmic X-ray sources has become a well-established technique over the last decade, with the wide variety of investigations performed with the diffraction grating spectrometers on Chandra and XMM-Newton. I will review some of the common themes that have emerged from these studies, which comprises observations of "sources" as varied as the intergalactic medium and the atmospheres of hot neutron stars. With the microcalorimeter spectrometer array on Astro-H, we will be making two more big steps: true imaging spectroscopy, and extension of the high resolution to the Fe K band. I will outline some of the issues we will encounter, against the background of possible discoveries we may make.