Clean　and　renewable　energy　is　developing　to　realize　the　sustainable　utilization　of　energy　and　the　harmonious　development　of　the　economy　and　society.　Microgrids　are　a　key　technique　for　applying　clean　and　renewable　energy.　The　operation　optimization　of　microgrids　has　become　an　important　research　field.　This　paper　reviews　the　developments　in　the　operation　optimization　of　microgrids.　We　first　summarize　the　system　structure　and　provide　a　typical　system　structure,　which　includes　an　energy　generation　system,　an　energy　distribution　system,　an　energy　storage　system　and　energy　end　users.　Then,　we　summarize　the　optimization　framework　for　microgrid　operation,　which　contains　the　optimization　objective,　decision　variables　and　constraints.　Next,　we　systematically　review　the　optimization　algorithms　for　microgrid　operations,　of　which　genetic　algorithms　and　simulated　annealing　algorithms　are　the　most　commonly　used.　Lastly,　a　literature　bibliometric　analysis　is　provided;　the　results　show　that　the　operation　optimization　of　microgrids　has　received　increasing　attention　in　recent　years,　and　developing　countries　have　shown　more　interest　in　this　field　than　developed　countries　have.　Finally,　we　highlight　future　research　challenges　for　the　optimization　of　the　operation　of　microgrids.