The　incineration　process　for　municipal　solid　waste　(MSW)　has　the　advantages　of　fast　speed,　in-situ　treatment,　high　capacity　reduction　rate,　and　energy　recyclability.　Among　them,　the　MSW　incineration　(MSWI)　based　on　mechanical　grate　furnaces　is　widely　used.　However,　the　diversity　of　MSW　components　and　living　habits,　and　the　time-varying　characteristic　due　to　differences　of　natural　environment,　and　frequent　fluctuations　in　incineration　conditions　due　to　operating　differences　and　equipment　failures,　etc.,　making　it　difficult　to　maintain　the　MSWI　process　operation　at　optimization　status.　Moreover,　it　is　difficult　to　detect　the　combustion　conditions　in　the　furnace　in　real　time　by　experimental　methods　and　to　verify　the　optimized　control　algorithm　developed　offline　in　terms　of　ensuring　the　safety　of　MSWI　process.　Thus,　it　is　very　important　to　construct　a　numerical　simulation　model　of　MSWI　process　close　to　actual　operating　conditions.　Aim　at　the　above　problems,　this　paper　reviews　the　numerical　simulation　method　of　MSWI　process　based　on　grate　furnace.　First,　the　MSWI　process　is　described.　Then,　the　numerical　simulation　methods　of　the　MSWI　process　based　on　commercial　software　and　self-developed　software　are　summarized,　and　the　advantages　and　disadvantages　of　each　method　are　pointed　out.　Then,　a　comparative　analysis　of　the　above　methods　is　given,　and　the　difficulties　are　given　out.　Finally,　the　current　status　of　numerical　simulation　is　summarized,　and　future　research　directions　and　development　prospects　are　given.　©　2020　Technical　Committee　on　Control　Theory,　Chinese　Association　of　Automation.