Anthropogenic carbon emissions associated with energy consumption are rapidly increasing. Such carbon emissions are further directly related to global climate change. Thus, reducing carbon emissions to mitigate global climate change has been attracting increasing attention. Energy production and energy consumption is linked by energy networks. The network-constrained energy flow leads to a virtual circulation of embedded carbon emissions. This paper introduces the concept and significance of carbon emission flow (CEF), which helps identify the relationship between carbon emissions and energy consumption. Challenges for extending the CEF from an electricity network to multiple energy systems (MES) are analyzed, and CEF models in both the electricity network and MES are summarized. The distribution of CEF and transfer of carbon emissions are studied using realistic case studies based on the energy interconnection system of Southeast Asia and real-world MES in the Jing-Jin-Ji economic circle. Considering the electricity trade in Southeast Asia in 2050, the results show that significant amounts of carbon emissions are transferred among countries. Approximately 19698 ktCO2 of carbon emissions in Malaysia are attributable to electricity demands of other countries. Conversely, the Philippines and Vietnam would be responsible for additional carbon emissions of 10620 ktCO2 and 42375 ktCO2, respectively. With the CEF model, carbon emissions in different energy sectors can be reasonably quantified, thus facilitating the allocation of emission reduction targets in climate change negotiations and low-carbon policymaking. Keywords: Carbon emission flow, Global climate change, Electricity network, Multiple energy systems