Carbapenem‐resistant Enterobacteriaceae (CRE) have been listed by the WHO as high‐priority pathogens owing to their high association with mortalities and morbidities. Resistance to multiple β‐lactams complicates effective clinical management of CRE infections. Using plasmid typing methods, a wide distribution of plasmid replicon groups has been reported in CREs around the world, including IncF, N, X, A/C, L/M, R, P, H, I, and W. We performed a literature search for English research papers, published between 2013 and 2018, reporting on plasmid‐mediated carbapenem resistance. A rise in both carbapenemase types and associated plasmid replicon groups was seen, with China, Canada, and the United States recording a higher increase than other countries. blaKPC was the most prevalent, except in Angola and the Czech Republic, where OXA‐181 (n = 50, 88%) and OXA‐48–like (n = 24, 44%) carbapenemases were most prevalent, respectively; blaKPC‐2/3 accounted for 70% (n = 956) of all reported carbapenemases. IncF plasmids were found to be responsible for disseminating different antibiotic resistance genes worldwide, accounting for almost 40% (n = 254) of plasmid‐borne carbapenemases. blaCTX‐M, blaTEM, blaSHV, blaOXA‐1/9, qnr, and aac‐(6′)‐lb were mostly detected concurrently with carbapenemases. Most reported plasmids were conjugative but not present in multiple countries or species, suggesting limited interspecies and interboundary transmission of a common plasmid. A major limitation to effective characterization of plasmid evolution was the use of PCR‐based instead of whole‐plasmid sequencing–based plasmid typing.