In a globalised world, the transfer of carbon between regions, either physically or embodied in production, represents a substantial fraction of global carbon emissions. The resulting emission transfers are important for balancing regional carbon budgets and for understanding the drivers of emissions. In this paper we synthesise current understanding in two parts: (1) CO₂ emissions embodied in goods and services that are produced in one country but consumed in others, and (2) carbon physically present in fossil fuels, petroleum-derived products, harvested wood products, crops, and livestock products. We describe the key differences between studies and provide a consistent set of estimates using the same definitions, modelling framework, and consistent data. We find the largest trade flows of carbon in international trade in 2004 were fossil fuels (2673 MtC, 37 % of global emissions), CO₂ embodied in traded goods and services (1661 MtC, 22 % of global emissions), crops (522 MtC, 31 % of total harvested crop carbon), petroleum-based products (183 MtC, 50 % of their total production), harvested wood products (149 MtC, 40 % of total roundwood extraction), and livestock products (28 MtC, 22 % of total livestock carbon). We find that for embodied CO₂ emissions, estimates from independent studies are robust, and that differences between individual studies are not a reflection of the uncertainty in consumption-based estimates, but rather these differences result from the use of different production-based emissions input data and different definitions for allocating emissions to international trade. After adjusting for these issues, results across independent studies converge to give less uncertainty than previously assumed. For physical carbon flows there are relatively few studies to be synthesised, but differences between existing studies are due to the method of allocating to international trade, with some studies using "apparent consumption" as opposed to "final consumption". While results across studies are sufficiently robust to be used in further applications, more research is needed to understand differences and to harmonise definitions for particular applications.