Direct　nitrous　oxide　(N2O)　emissions　for　wastewater　treatment　contribute　significantly　to　the　carbon　footprint.　Mathematical　and　machine　learning　models　enable　dynamic　simulations　of　N2O　production,　degradation　and　release,　offering　insights　for　mitigating　carbon　emissions.　This　article　uses　CiteSpace　bibliometric　software　to　analyze　the　evolution　of　N2O　emission　models　from　2000　to　the　present,　highlighting　the　modeling　processes　and　methods　of　both　approaches.　Between　2000　and　2014,　mathematical　models　for　lab-scale　and　pilot-scale　WWTPs　matured　rapidly.　From　2015　to　2021,　mathematical　models　improved,　while　machine　learning　expanded　to　a　broader　range　of　WWTPs　and　new　treatment　processes.　Since　2022,　machine　learning　has　advanced　rapidly　to　address　N2O　emission　challenges.　Mathematical　models　are　useful　when　data　is　limited　and　effective　for　short-term　simulations,　though　they　require　detailed　input　partitioning　and　are　prone　to　empirical　modeling.　Machine　learning　excels　in　simulating　long-term　emissions　but　relies　on　large　datasets,　lacks　sufficient　interpretability,　and　requires　high　algorithmic　expertise.　The　integration　of　process-based　mathematical　models　with　machine　learning　may　become　a　future　research　focus,　necessitating　specific　coupling　methods.　©　2025　Elsevier　Ltd