We discuss how future X-ray instruments which are under development can contribute to our understanding of the non-thermal Universe. Much progress has been made in the field of X-ray Astronomy recently, thanks to the operation of modern X-ray telescopes such as Chandra, XMM-Newton, Suzaku, and Swift, but more in-depth investigation awaits future missions. These future missions include ASTROSAT, NuStar, e-ROSITA, ASTRO-H and GEMS, which will be realized in the next decade, and also much larger projects such as Athena and LOFT, which have been proposed for the 2020's. All of those are expected to bring a variety of novel observational results regarding astrophysical sources of high-energy particles and radiation, i.e. supernova remnants, neutron stars, stellar-mass black holes, active galaxies, and clusters of galaxies among others. The operation of the future X-ray instruments will proceed in parallel with the operation of Fermi-LAT and the Cherenkov Telescope Array. We emphasize that the synergy between the X-ray and gamma-ray observations is particularly important, and that the planned X-ray missions, when in conjunction with the modern gamma-ray observatories, will indeed provide a qualitatively better insight into the high-energy Universe.

18 pages, 15 figures. Accepted for publication in the Astroparticle Physics, Special Issue on Physics with the Cherenkov Telescope Array (editors: J. Hinton, S. Sarkar, & D.F. Torres)