King Messiah will arise in the future and will restore the kingship of David to its ancient condition, to its rule as it was at first. And he will rebuild the Temple and gather the exiled of Israel. And in his days all the laws will return as they were in the past. They will offer up sacrifices, and will observe the Sabbatical years and the jubilee years with regard to all the commandments stated in the Tora. And he who does not believe in him, or he who does not await his coming, denies not only the [other] prophets, but also the Tora and Moses our Master. For, behold, the Tora testifies about him [the Messiah], as it is written, The Lord will return your captivity and have compassion upon thee, and will return and gather thee from all the peoples whither the Lord thy God hath scattered thee. If any of thine that are dispersed be in the uttermost parts of heaven, from thence will the Lord thy God gather thee, and from thence will He fetch thee. And the Lord thy God will bring thee into the land which thy fathers possessed and thou shalt possess it (Deut. 30:3-5).
And these are things which are explicitly stated in the Tora, and they comprise all the things which were said by the prophets. Even in the section "Balaam" it is said and there he prophesied about the two Messiahs: about the first Messiah who was David, who saved Israel from the hands of its enemies, and about the last Messiah, who will arise from among David's children and who will save Israel at the End. And there he says: I see him but not now (Num. 24: 17), this refers to David; I behold him but not nigh (ibid.), this refers to King Messiah; A star shall step forth out of Jacob (ibid.), this refers to David; and a scepter shall rise out of Israel (ibid.), this refers to King Messiah. . . .
And think not that the Messiah must perform signs and portents and bring about new things in the world, or that he will resuscitate the dead, or the like. Not so. For, behold, R. Akiba was one of the greatest of the sages of the Mishna, and he was a follower of King Ben Koziba [Bar Kokhba], and he said about him that he was King Messiah. And he and the sages of his generation thought that he was King Messiah, until he was slain because of the sins. As soon as he was slain it became evident to them that he was not the Messiah. And the sages had asked of him neither a sign nor a portent. And the essence of the matter is that the laws and ordinances of this Tora are forever and ever, and one must neither add to them nor subtract from them.
And if there should arise from the House of David a king who studies the Tora and occupies himself with the commandments as his father David had, according to the written and the oral Tora; and if he forces all Israel to follow the Tora and observe its rules; and if he fights the wars of the Lord-then he must be presumed to be the Messiah. And if he succeeds in his acts, and rebuilds the Temple in its place, and gathers the exiled of Israel - then he certainly is the Messiah. And he will repair the whole world to serve the Lord together, as it is written, For then will I turn to the peoples a pure language that they may all call upon the name of the Lord to serve Him with one consent (Zeph. 3:9).
It should not come to one's mind that in the days of the Messiah anything in the customary order of the world will be annulled, or that there will be something new in the order of Creation. For the world will continue in its path. And that which Isaiah said, The wolf shall dwell with the lamb, and the leopard shall lie down with the kid (Isa. 11:6), is but an allegory and a riddle. The true meaning of it is that Israel will dwell in safety with the wicked of the idolaters who are likened to a wolf and a leopard. . . . And all of them will return to the faith of truth, and they will neither rob nor despoil, but will eat the things which are permitted, in pleasure, together with Israel, as it is written, The lion shall eat straw like the ox (lsa. 11:7). And likewise, all the similar things said about the Messiah are but allegories. And in the days of the Messiah it will become known to everybody what thing the allegory signified and to what thing it alluded.
The sages said that the only difference between this world and the days of the Messiah will be with regard to the enslavement to the kingdoms. It appears from the plain meaning of the words of the prophets that at the beginning of the days of the Messiah, there will be the war of Gog and Magog. And that prior to the war of Gog and Magog, a prophet will arise to straighten Israel and to prepare their hearts, as it is written, Behold, I will send to you Elijah the prophet before the coming of the great and terrible day of the Lord (Mal. 3:23). And he will come not to declare the pure impure, or the impure pure; nor to declare unfit those who are presumed to be fit, nor to declare fit those who are held to be unfit; but for the sake of peace in the world. . . . And there are those among the sages who say that prior to the coming of the Messiah will come Elijah. But all these things and their likes, no man can know how they will be until they will be. For they are indistinct in the writings of the prophets. Neither do the sages have a tradition about these things. It is, rather, a matter of interpretation of the Biblical verses. Therefore there is a disagreement among them regarding these matters. And in any case, these things are mere details which are not of the essence of the faith. And one should definitely not occupy oneself with the matter of legends, and should not expatiate about the midrashim that deal with these and similar things. And one should not make essentials out of them. For they lead neither to fear nor to love [of God]. Neither should one calculate the End. The sages said, "May the spirit of those who calculate the End be blown away." But let him wait and believe in the matter generally, as we have explained.

In the days of King Messiah, when his kingdom is established and all Israel are gathered into it, the descent of all of them will be confirmed by him through the Holy Spirit which will rest upon him, as it is written, And he shall sit as a refiner and purifier of silver, and he shall purify the sons of Levi, and purge them as gold and silver (Mal. 3:3). And he will first purify the Children of Levi and will say: "This is of priestly descent, and this is of Levitic descent." And he will reject those who are not descended of Israel, as it is written, And the Tirshatha [governor] said to them that they should not eat the most holy things till there stood up a priest with U rim and Thummim (Ezra 2:63). From this you learn that the presumption of descent will be confirmed, and those with established descent will be announced by the Holy Spirit. And he will establish the descent not from Israel [in general] but from each tribe and tribe. For he will announce that this one is from such and such a tribe, and this one from such and such a tribe. . . .

The sages and the prophets yearned for the days of the Messiah not in order that they should rule over the whole world, and not in order that they should lord it over the idolaters, and not in order that the nations should elevate them, and not in order that they should eat and drink and rejoice; but in order that they should devote themselves to the Tora and its wisdom, and that there be nobody to oppress them and to negate, so that they should merit life in the World to Come....

And in that time there will be neither hunger nor war, neither jealousy nor competition, but goodness will spread over everything. And all the delights will be as common as dust. And the whole world will have no other occupation but only to know the Lord. And therefore Israel will be great sages, and knowers of secret things, and they will attain a knowledge of their Creator as far as the power of man allows, as it is written, For the earth shall be full of the knowledge of the Lord, as the waters cover the sea (lsa. 11:9).

(Maimonides, Yad haHazaqa, Shoftim, Hilkhot M'lakhim 11-12)

Source: Raphael Patai, The Messiah Texts, Wayne State University Press