A　multipath　error　is　one　of　the　main　sources　of　GNSS　positioning　errors.　It　cannot　be　eliminated　by　forming　double-difference　and　other　methods,　and　it　has　become　an　issue　in　GNSS　positioning　error　processing,　because　it　is　mainly　related　to　the　surrounding　environment　of　the　station.　To　address　multipath　errors,　three　main　mitigation　strategies　are　employed:　site　selection,　hardware　enhancements,　and　data　processing.　Among　these,　data　processing　methods　have　been　a　focal　point　of　research　due　to　their　cost-effectiveness,　impressive　performance,　and　widespread　applicability.　This　paper　focuses　on　the　review　of　data　processing　mitigation　methods　for　GNSS　carrier-phase　multipath　errors.　The　paper　begins　by　elucidating　the　origins　and　mitigation　strategies　of　multipath　errors.　Subsequently,　it　reviews　the　current　research　status　pertaining　to　data　processing　methods　using　stochastic　and　functional　models　to　counter　multipath　errors.　The　paper　also　provides　an　overview　of　filtering　techniques　for　extracting　multipath　error　models　from　coordinate　sequences　or　observations.　Additionally,　it　introduces　the　evolution　and　algorithmic　workflow　of　sidereal　filtering　(SF)　and　multipath　hemispherical　mapping　(MHM),　from　both　coordinate　and　observation　domain　perspectives.　Furthermore,　the　paper　emphasizes　the　practical　significance　and　research　relevance　of　multipath　error　processing.　It　concludes　by　delineating　future　research　directions　in　the　realm　of　multipath　error　mitigation.