The ratio of the stable carbon isotopes of atmospheric CO2 (δ13CO2) contains valuable information on the processes which are operating on the global carbon cycle. However, current δ13CO2 ice core records are still limited in both resolution and temporal coverage, as well as precision. In this study we performed simulations with the carbon cycle box model BICYCLE with special emphasis on atmospheric δ13CO2, proposing how changes in δ13CO2 might have evolved over the last 740,000 years. We furthermore analyze the relationship between atmospheric δ13CO2, pCO2, and deep ocean δ13C of dissolved inorganic carbon (DIC) (δ13CDIC) in both our modeling framework and proxy records (when available). Our analyses show that mean ocean and deep Pacific δ13CDIC are mainly controlled by the glacial/interglacial uptake and release of carbon temporarily stored in the terrestrial biosphere during warmer climate periods. In contrast glacial/interglacial changes in pCO2 and δ13CO2 represent mainly a mixture of ocean-related processes superimposed on the slow glacial/interglacial change in terrestrial carbon storage. The different processes influencing atmospheric δ13CO2 largely compensate each other and cancel all variability with frequencies of 1/100 kyr-1. Large excursions in δ13CO2 can a priori be expected, as any small phase difference between the relative timing of the dominant and opposite sign processes might create large changes in δ13CO2. Amplitudes in δ13CO2 caused by fast terrestrial uptake or release during millennial-scale climate variability depend not only on the amount of transferred carbon but also on the speed of these changes. Those which occur on timescales shorter than a millennium are not detectable in δ13CO2 because of gas exchange equilibration with the surface ocean. The δ13CO2 signal of fast processes, on the other hand, is largely attenuated in ice core records during the firnification and gas enclosure. We therefore suggest to measure δ13CO2 with priority on ice cores with high temporal resolution and select times with rather fast climatic changes.