In this "Grand Challenges" paper, we review how the carbon isotopic composition of atmospheric CO2 has changed since the Industrial Revolution due to human activities and their influence on the natural carbon cycle, and we provide new estimates of possible future changes for a range of scenarios. Emissions of CO2 from fossil fuel combustion and land use change reduce the ratio of 13C/12C in atmospheric CO2 (δ13CO2). This is because 12C is preferentially assimilated during photosynthesis and δ13C in plant-derived carbon in terrestrial ecosystems and fossil fuels is lower than atmospheric δ13CO2. Emissions of CO2 from fossil fuel combustion also reduce the ratio of 14C/C in atmospheric CO2 (Δ14CO2) because 14C is absent in million-year-old fossil fuels, which have been stored for much longer than the radioactive decay time of 14C. Atmospheric Δ14CO2 rapidly increased in the 1950s to 1960s because of 14C produced during nuclear bomb testing. The resulting trends in δ13C and Δ14C in atmospheric CO2 are influenced not only by these human emissions but also by natural carbon exchanges that mix carbon between the atmosphere and ocean and terrestrial ecosystems. This mixing caused Δ14CO2 to return toward preindustrial levels in the first few decades after the spike from nuclear testing. More recently, as the bomb 14C excess is now mostly well mixed with the decadally overturning carbon reservoirs, fossil fuel emissions have become the main factor driving further decreases in atmospheric Δ14CO2. For δ13CO2, in addition to exchanges between reservoirs, the extent to which 12C is preferentially assimilated during photosynthesis appears to have increased, slowing down the recent δ13CO2 trend slightly. A new compilation of ice core and flask δ13CO2 observations indicates that the decline in δ13CO2 since the preindustrial period is less than some prior estimates, which may have incorporated artifacts owing to offsets from different laboratories' measurements. Atmospheric observations of δ13CO2 have been used to investigate carbon fluxes and the functioning of plants, and they are used for comparison with δ13C in other materials such as tree rings. Atmospheric observations of Δ14CO2 have been used to quantify the rate of air-sea gas exchange and ocean circulation, and the rate of net primary production and the turnover time of carbon in plant material and soils. Atmospheric observations of Δ14CO2 are also used for comparison with Δ14C in other materials in many fields such as archaeology, forensics, and physiology. Another major application is the assessment of regional emissions of CO2 from fossil fuel combustion using Δ14CO2 observations and models. In the future, δ13CO2 and Δ14CO2 will continue to change. The sign and magnitude of the changes are mainly determined by global fossil fuel emissions. We present here simulations of future δ13CO2 and Δ14CO2 for six scenarios based on the shared socioeconomic pathways (SSPs) from the 6th Coupled Model Intercomparison Project (CMIP6). Applications using atmospheric δ13CO2 and Δ14CO2 observations in carbon cycle science and many other fields will be affected by these future changes. We recommend an increased effort toward making coordinated measurements of δ13C and Δ14C across the Earth System and for further development of isotopic modeling and model-data analysis tools.