Using a numerical model of the global carbon cycle and constraints from various geochemical parameters, we illustrate various scenarios (e.g., methane vs. volcanic carbon dioxide outgassing events, increases and decreases in global river fluxes) that produce carbon isotopic variations in the sedimentary record. In particular, using reasonable constraints, it is very difficult to produce a large positive carbon isotope excursion. Large positive carbon isotope excursions recorded in marine carbonates and organic carbon are commonly cited as evidence for increased organic carbon burial rates and formation of widespread "black shales." However, a greatly increased burial flux of organic carbon need not be manifested as black shale and does not necessarily produce a positive carbon isotope excursion. Negative carbon isotope excursions have recently received considerable attention because it can be argued that they are produced by episodes of methane release from gas hydrate reservoirs. Such excursions can have other explanations, however, and can be produced by volcanic events, as we will show. In some cases, short-term negative carbon isotope excursions are followed by large positive excursions (e.g., Aptian, Toarcian) leading to the intriguing proposal that methane degassing events trigger oceanic anoxic events (OAEs). Although plausible, we will demonstrate that other combinations of mechanisms and feedbacks produce similar signals. We also will outline hypotheses to account for long-term episodes of positive isotope values (+7 permil) in the Neoproterozoic and Paleoproterozoic without sustaining high rates of organic carbon burial.