What are the criteria that Judaism has established about the messiah?
The Jewish tradition of "The Messiah" has its foundation in numerous biblical references, and understands "The Messiah" to be a human being - without any overtone of deity or divinity - who will bring about certain changes in the world and fulfill certain criteria before he can be acknowledged as "The Messiah".
First of all, he must be Jewish - "...you may appoint a king over you, whom the L-rd your G-d shall choose: one from among your brethren shall you set as king over you." (Deuteronomy 17:15)
He must be a member of the tribe of Judah - "The staff shall not depart from Judah, nor the sceptre from between his feet..." (Genesis 49:10)
He must be a direct male descendant of King David and King Solomon, his son - "And when your days (David) are fulfilled, and you shall sleep with your fathers, I will set up your seed after you, who shall issue from your bowels, and I will establish his kingdom. He shall build a house for my name, and I will make firm the throne of his kingdom forever..." (2 Samuel 7:12 - 13)
He must gather the Jewish people from exile and return them to Israel -"And he shall set up a banner for the nations, and shall assemble the outcasts of Israel, and gather together the dispersed of Judah from the four corners of the earth." (Isaiah 11:12)
He must rebuild the Temple in Jerusalem - "...and I will set my sanctuary in their midst forever and my tabernacle shall be with them.." (Ezekiel 37:26 - 27)
He will rule at a time of world-wide peace - "...they shall beat their swords into plowshares, and their spears into pruning hooks; nation shall not lift up sword against nation, neither shall they learn war anymore." (Micah 4:3)
He will rule at a time when the Jewish people will observe G-d's commandments - "My servant David shall be king over them; and they shall all have one shepherd. They shall follow My ordinances and be careful to observe My statutes." (Ezekiel 37:24)
He will rule at a time when all people will come to acknowledge and serve one G-d - "And it shall come to pass that from one new moon to another and from one Sabbath to another, shall all flesh come to worship before Me, says the L-rd" (Isaiah 66:23)
All of these criteria are best stated in the book of Ezekiel Chapter 37 verses 24-28:
And David my servant shall be king over them; and they shall all have one shepherd. they shall also follow My judgments and observe My statutes, and do them. And they shall dwell in the land that I have given to Yaakov my servant, in which your fathers have dwelt and they shall dwell there, they and their children, and their children's children forever; and my servant David shall be their prince forever. Moreover, I will make a covenant of peace with them, it shall be an everlasting covenant with them, which I will give them; and I will multiply them and I will set my sanctuary in the midst of them forevermore. And my tabernacle shall be with them: and I will be their G-d and they will be my people. Then the nations shall know that I am the L-rd who sanctifies Israel, when My sanctuary will be in the midst of them forevermore.
If an individual fails to fulfill even one of these conditions, then he cannot be "The Messiah." A careful analysis of these criteria shows us that to date, no one has fulfilled every condition.