Supernova remnants (SNRs) play a fundamental role in the evolution of galaxies; they are main providers of heavy elements, inject thermal energies into the interstellar medium, and are believed to be the birth places of cosmic rays up to the "knee (3e15 eV)". In addition, their large sizes allow us to reveal detailed explosion geometries, which is a key to understand SN explosion mechanisms. SNRs are also excellent sites to investigate physics of collisionless shocks that are ubiquitous in the universe. High-resolution (E/dE >~ 100) X-ray spectroscopy is essential to obtain deep insight into all of the topics listed above, and is expected to open other new subfields of SNR physics. It has been thought that this can be best achieved with the upcoming micro-calorimeter onboard ASTRO-H. However, we show that grating instruments onboard XMM-Newton and Chandra in orbit are also strong tools for high-resolution X-ray spectroscopy, despite both instruments are slitless and are generally considered to be useless for diffuse sources like SNRs. In this talk, a particular emphasis will be given to our recent XMM-Newton observations of the Puppis~A SNR, which is one of the brightest core-collapsed SNRs in our Galaxy. The talk will be closed by presenting prospects for ASTRO-H.