This is an extensive subject and much can be found on it within LDS Teachings and Doctrines, including in Jesus The Christ by James E. Talmage, from where I have summarised the following:
The date of the future advent of Christ has never been revealed to man. To the inquiring Apostles who laboured with the Master, He said: "But of that day and hour knoweth no man, no, not the Angels of heaven, but my Father only." In the present age, a similar declaration has been made by the Father: "I, the Lord God, have spoken it, but the hour and the day no man knoweth, neither the Angels in heaven, nor shall they know until He comes." He says to His Elders: Go ye into all the world and preach the Gospel to every creature; and after your testimony cometh wrath and indignation upon the people if this message is rejected; God will bring judgments upon the world until He has humbled the people to a state where they will be glad to receive it. The judgments of God shall stalk through the earth, decimating the human race, before the great day of the Lord shall come. Wars and rumours of wars, famine and pestilence, the voice of thunderings, and the voice of lightnings, and the voice of tempests, and the voice of the waves of the sea, heaving themselves beyond their bounds. The earth shall tremble and reel to and fro as a drunken man, that shall cause groanings in the midst of her, and men shall fall upon the ground, and shall not be able to stand. and the sun shall hide his face, and shall refuse to give light, and the moon shall be bathed in blood, and the stars shall become exceeding angry, and shall cast themselves down as a fig that falleth from off a fig tree. All things shall be in commotion; and surely, men's hearts shall fail them; for fear shall come upon all people. Fearful indeed will it be to individuals, families, and nations, who have so far sunk into sin as to have forfeited their claim to mercy. The time is not that of the final judgment--when the whole race of mankind shall stand in the resurrected state before the bar of God--nevertheless it shall be a time of unprecedented blessing unto the righteous, and of condemnation and vengeance upon the wicked.
With Christ shall come those who have already been resurrected; and His approach shall be the means of inaugurating a general resurrection of the righteous dead, while the pure and just who are still in the flesh shall be instantaneously changed from the mortal to the immortal state and shall be caught up with the newly resurrected to meet the Lord and His celestial company, and shall descend with Him. The coming of Christ in the last days, accompanied by the apostles of old and by the resurrected saints, is to mark the establishment of the Kingdom of Heaven upon earth. The faithful apostles who were with Jesus in His earthly ministry are to be enthroned as judges of the whole house of Israel; they will judge the Nephite Twelve, who in turn will be empowered to judge the descendants of Lehi, or that branch of the Israelitish nation which was established upon the western continent. The Kingdom of God is the Church established by divine authority upon the earth; this institution asserts no claim to temporal rule over nations; its sceptre of power is that of the Holy Priesthood, to be used in the preaching of the Gospel and in administering its ordinances for the salvation of mankind living and dead. The Kingdom of Heaven is the divinely ordained system of government and dominion in all matters, temporal and spiritual; this will be established on earth only when its rightful Head, the King of kings, Jesus the Christ, comes to reign. His administration will be one of order, operated through the agency of His commissioned representatives invested with the Holy Priesthood. When Christ appears in His glory, and not before, will be realised a complete fulfilment of the supplication: "Thy kingdom come. Thy will be done in earth, as it is in heaven." The Kingdom of God has been established among men to prepare them for the Kingdom of Heaven which shall come; and in the blessed reign of Christ the King shall the two be made one. The keys of the kingdom of God are committed unto man on the earth, and from thence shall the Gospel roll forth unto the ends of the earth, as the stone which is cut out of the mountain without hands until it has filled the whole earth; that the inhabitants thereof may receive it, and be prepared for the days to come, in the which the Son of man shall come down in heaven, clothed in the brightness of his glory, to meet the kingdom of God which is set up on the earth; Wherefore may the kingdom of God go forth, that the kingdom of heaven may come.