Carbon Emissions Pinch Analysis (CEPA) is a branch of Process Integration (PI) that was developed as a systematic methodology for planning the optimal allocation of energy to various demands under carbon-constrained conditions. Since its inception in 2007, the body of CEPA literature has branched out into distinct areas. The first branch consists of direct applications of CEPA to specific geographic regions or nations, which includes early applications in Ireland and New Zealand, leading to more recent applications to parts of China and the United States. The second branch consists of methodological extensions of the original graphical CEPA procedure. These developments include algebraic and Mathematical Programming (MP) variants. The third branch of CEPA literature extends its principles to other measures of sustainability, such as various environmental footprints; recent attempts to allow the methodology to simultaneously handle multiple sustainability metrics have also been published. Finally, in the fourth branch, CEPA has also been extended to handle special problem structures such as segregated targeting for multiple geographic zones, or deployment of CO2 capture and storage (CCS). Also included here are CEPA variants for carbon-constrained planning at different levels, ranging from enterprise scale, to supply chains and sector level (e.g., transportation or waste disposal), and finally to economy-wide analysis when integrated with established tools such as Input-Output Analysis (IOA). This paper discusses key developments in CEPA literature, with emphasis on the most recent developments (2016 to the present), as well as further prospects for the development of this PI sub-area.