Here we describe a new study of the supernova remnants (SNRs) and SNR candidates in nearby face-on spiral galaxy M83, based primarily on MUSE integral field spectroscopy. Our revised catalog of SNR candidates in M83 has 366 objects, 81 of which are reported here for the first time. Of these, 229 lie within the MUSE observation region, 160 of which have spectra with [SII]:H{alpha} ratios exceeding 0.4, the value generally accepted as confirmation that an emission nebula is shock-heated. Combined with 51 SNR candidates outside the MUSE region with high [SII]:H{alpha} ratios, there are 211 spectroscopically confirmed SNRs in M83, the largest number of confirmed SNRs in any external galaxy. MUSE's combination of relatively high spectral resolution and broad wavelength coverage has allowed us to explore two other properties of SNRs that could serve as the basis of future SNR searches. Specifically, most of the objects identified as SNRs on the basis of [SII]:H{alpha} ratios exhibit more velocity broadening and lower ratios of [SIII]:[SII] emission than HII regions. A search for nebulae with the very broad emission lines expected from young, rapidly expanding remnants revealed none, except for the previously identified B12-174a. The SNRs identified in M83 are, with few exceptions, middle-aged interstellar medium (ISM) dominated ones. Smaller-diameter candidates show a larger range of velocity broadening and a larger range of gas densities than the larger-diameter objects, as expected if the SNRs expanding into denser gas brighten and then fade from view at smaller diameters than those expanding into a more tenuous ISM.