Comets are considered the most primitive planetary bodies in our Solar System, i.e., they should have best preserved the solid components of the matter from which our Solar System formed. ESA’s recent Rosetta mission to Jupiter family comet 67P/Churyumov–Gerasimenko (67P/CG) has provided a wealth of isotope data which expanded the existing data sets on isotopic compositions of comets considerably. In this paper we review our current knowledge on the isotopic compositions of H, C, N, O, Si, S, Ar, and Xe in primitive Solar System materials studied in terrestrial laboratories and how the Rosetta data acquired with the ROSINA (Rosetta Orbiter Sensor for Ion and Neutral Analysis) and COSIMA (COmetary Secondary Ion Mass Analyzer) mass spectrometer fit into this picture. The H, Si, S, and Xe isotope data of comet 67P/CG suggest that this comet might be particularly primitive and might have preserved large amounts of unprocessed presolar matter. We address the question whether the refractory Si component of 67P/CG contains a presolar isotopic fingerprint from a nearby Type II supernova (SN) and discuss to which extent C and O isotope anomalies originating from presolar grains should be observable in dust from 67P/CG. Finally, we explore whether the isotopic fingerprint of a potential late SN contribution to the formation site of 67P/CG in the solar nebula can be seen in the volatile component of 67P/CG.