Supernova remnants (SNRs) are the aftermath of stellar explosions, which inject large amounts of energy into the interstellar medium (ISM), carving out new structures and transferring kinetic energy to the ISM. They also act as recycling centers, which return elements processed in stars to the ISM, and cosmic particle accelerators. The evolution of SNRs can be best studied in soft X-ray line and continuum emission, since they mainly consist of very hot plasma (106-107 K). While it is difficult to observe these soft X-ray sources in our own Galaxy due to absorption by matter in the Galactic plane, the Magellanic Clouds as well as the nearby spiral galaxies M 31 and M 33 are ideal targets to study both particular SNRs in detail and the SNR population in a galaxy as a whole. Various studies of SNRs in the Local Group galaxies have been carried out with XMM-Newton or Chandra since the launch of the mission, and in the coming years the new X-ray all-sky survey performed with eROSITA will provide us with more complete data of SNRs in the nearby Universe to low flux limits.