Moving　least　squares(MLS)　is　a　common　method　of　data　fitting,　and　it　has　a　high　degree　of　flexibility　and　precision　that　is　significantly　better　than　other　fitting　methods.　This　paper　introduces　the　principle　of　MLS,　enumerates　the　important　research　progress　in　recent　years　at　home　and　abroad,　and　analyzes　the　advantages　of　the　method　applied　in　data　fitting　tasks.　MLS　also　has　problems　such　as　susceptibility　equations,　support　domain　and　weight　function　selection　relying　on　empirical　judgment.　The　researchers　put　forward　some　strategies　for　the　problem,　but　they　have　not　solved　it　fundamentally.　For　the　future　research　direction,　this　paper　suggests　that　the　researchers　should　study　in　depth　from　the　mathematical　theory,　convergence,　error　analysis　and　performance　comparison　of　MLS　method　and　its　improved　methods.