I believe that when Christ comes to the earth, He is going to be governing it. He is going to direct his people in his ways to accomplish his tasks.  
 
Here's what is said about the Millennium in the Church Published Book "Gospel Principles" (Chapter 44) 
 
"Righteous Government: 
 
Jesus Christ will not only lead the Church during the Millennium, but he will also be in charge of the political government. This government will be based on principles of righteousness and will preserve the basic rights and freedoms of all people. Mortals, both members of the Church and nonmembers, will hold government positions (see Brigham Young, in Journal of Discourses, 2:310). They will receive help from resurrected beings. At this time there will be two capitals in the world, one in Jerusalem, the other in America (see Joseph Fielding Smith, Doctrines of Salvation, 3:66–72). “For out of Zion shall go forth the law, and the word of the Lord from Jerusalem” (Isaiah 2:3)."