As the observable products of explosive stellar death, supernova remnants reveal some of the most direct information on the physics of the explosions, the properties of the progenitor systems, and the demographics of compact objects formed in the supernova events. High sensitivity X-ray observations have allowed us to probe the properties of the shocked plasma, providing constraints on abundances and ionization states that connect directly progenitor masses and metallicities, the nature of the explosions (core-collapse vs. thermonuclear), and the physics of shock heating and particle acceleration in fast shocks. Studies of SNRs in the Magellanic Clouds have provided information on source demographics in a low metallicity environment, and deep searches for point sources in Galactic SNRs imply that many remnants contain rapidly cooling neutron stars or black holes. Based on Chandra observations, we know that crucial measurements required to advance our knowledge in these areas are possible only with much more sensitive observations at high angular resolution. From identifying the effects of particle acceleration on the post-shock gas in young SNRs like Tycho to obtaining spatially resolved spectra - and identifying compact objects - for young SNRs in the Magellanic Clouds, the capabilities of a facility like the X-ray Surveyor are required. Here I present a summary of recent advances brought about by spectral investigations of SNRs, and discuss particular examples of new advances that will be enabled by X-ray Surveyor capabilities.