We present a model of the global primary plastic trade network (GPPTN) and report estimates of embodied impacts including greenhouse gas (GHG) emissions, cumulative fossil energy demand, and embedded carbon. The network is constructed for 11 thermoplastic resins that account for the majority of global primary plastic trade. A total of 170 million metric tonnes (Mt) of primary plastics were traded in 2018, responsible for 350 Mt of embodied GHG emissions, 8.9 exajoules (EJ) of cumulative fossil energy demand and 95 Mt of embedded carbon. In 2018, embodied GHG emissions for GPPTN were comparable to annual carbon dioxide emissions of developed nations like Italy and France. The cumulative fossil energy demand of GPPTN was equivalent to 1.5 trillion barrels of crude oil and the carbon embedded in GPPTN was equivalent to carbon in 118 Mt of natural gas or 109 Mt of petroleum. Statistical inference and network measures provide evidence that a few key trade relationships account for a majority of plastic flows and subsequent embodied impacts through the network. The significant embodied impacts and materials in GPPTN must be considered going forward as policies are developed to improve the circularity and environmental sustainability of the plastics industry.