{Reference Type}: Journal Article {Title}: A review on mathematical modeling of microbial and plant induced permafrost carbon feedback. {Author}: Fasaeiyan N;Jung S;Boudreault R;Arenson LU;Maghoul P; {Journal}: Sci Total Environ {Volume}: 939 {Issue}: 0 {Year}: 2024 Aug 20 {Factor}: 10.753 {DOI}: 10.1016/j.scitotenv.2024.173144 {Abstract}: This review paper analyses the significance of microbial activity in permafrost carbon feedback (PCF) and emphasizes the necessity for enhanced modeling tools to appropriately predict carbon fluxes associated with permafrost thaw. Beginning with an overview of experimental findings, both in situ and laboratory, it stresses the key role of microbes and plants in PCF. The research investigates several modeling techniques, starting with current models of soil respiration and plant-microorganism interactions built outside of the context of permafrost, and then moving on to specific models dedicated to PCF. The review of the current literature reveals the complex nature of permafrost ecosystems, where various geophysical factors have considerable effects on greenhouse gas emissions. Soil properties, plant types, and time scales all contribute to carbon dynamics. Process-based models are widely used for simulating greenhouse gas production, transport, and emissions. While these models are beneficial at capturing soil respiration complexity, adjusting them to the unique constraints of permafrost environments often calls for novel process descriptions for proper representation. Understanding the temporal coherence and time delays between surface soil respiration and subsurface carbon production, which are controlled by numerous parameters such as soil texture, water content, and temperature, remains a challenge. This review highlights the need for comprehensive models that integrate thermo-hydro-biogeochemical processes to understand permafrost system dynamics in the context of changing climatic circumstances. Furthermore, it emphasizes the need for rigorous validation procedures to reduce model complexity biases.