In Jewish thought, the redemption is divided into phases. There are disagreements on what order the phases will be in, but in general, what we expect that will happen:
All of the Jewish People will be gathered from around the world to the Land of Israel. The state there will be governed according to Jewish law and led by the Jewish king, often referred to as "the Messiah". He will defeat Israel's enemies and establish peace in the world (note: he will not rule the world, only the Jewish people. The nations will still govern themselves). The Jews will rebuild the Temple in Jerusalem. There will be universal recognition of God, and people from the nations will come to Jerusalem to worship. The Jews will fulfill their roles as teachers of mankind, while the other nations will fulfill the various roles they were tasked with by God. Each nation has its own duty in the world. And at some point far into the future of the redeemed world, the world will transition into The-World-To-Come.