In the days of the messiah nothing in the current reality will change except that Israel will have political sovereignty -Rambam (Maimonides, 1135-1204) Commentary to Mishnah Sanhedrin 10:1
It is true that in the days of the fulfillment of the mitzvot [i.e., when the messiah comes] the Land of Israel will be like the world in the beginning before the sin of the first man. No more will there be animals that kill -Ramban (Nachmanides, 1194-1270), Commentary on Leviticus 26:6
Before Zionism, in the middle ages, there was no consensus on just what the restored Israel would look like. The debate between the pro- and anti-Maimonideans reached the level of book-burning. Maimonides claimed that the only difference between the present reality and the messianic age would be the restoration of Jewish political sovereignty: we would be relieved of the yoke of oppression by the nations, and would be free to study Torah and live according to it. This flew in the face of the popular conception of a re-born world, in which lions would really lie down with lambs etc.
Even if we see Maimonides' view as relatively a rational and realistic understanding of redemption in history, still, it brings us to the classical Orthodox belief that anticipates a return to the good old days when David ruled and the Temple stood a Jewish sovereign state with the Temple sacrificial cult conducted by the descendants of Aaron as the official religion. That is the vision of the future/past repeated daily in the traditional liturgy. To this end there are institutions today dedicated to clarifying the exact details of the ritual objects of the Temple, from the measurements of the menorah to the recipe for techelet dye. To this end we keep track of who is a cohen. And of course, once the kingdom is established, it will be governed by Torah law. It is easy to dismiss this version of restored utopia as a romantic dream, a fantasy nurtured by two thousand years of remembering and longing. However, there seem to be many people who believe literally in this vision and not a few who are willing to take action even violent action in order to bring it closer to realization. In this view the boundaries of the restored kingdom will reflect not merely the maximum extent of the biblical monarchy, but the prophetic promise of "from the river of Egypt to the Euphrates."
The restoration of a biblical kingdom relieves us of having to wrestle with the moral dilemmas that beset sovereign states today from who gets to vote to whose phone can be tapped. David's monarchy existed before minority rights and individual freedoms were concerns of government. Democracy was a long way off. David (or God) invented what later became known as the divine right of kings. Wiping out a tribe or a nation, subjugating them as slaves, converting them by force these were all considered perfectly legitimate options, methods used by Israel and others in ancient times without giving rise to commissions of inquiry or international tribunals or boycotts. Presumably, a restoration of such a kingdom implies a restoration of the ambient world view of the period, relieving us of having to worry about new ideas that have developed since then. Mark Twain's Connecticut Yankee took his 19th century democratic values back with him into the middle ages and tried to implement them there. But it seems that there is a strand in our tradition that aspires to bring biblical society back to life in the post-modern world, implementing ancient values in our own time, overruling, or erasing, the accretions of law and value that have accumulated in the interim.
It is easy to see why this is a tempting prospect, and why it is hard to hold back from trying to live out this approach even in advance of the final redemption. But can we really forget what we have learned from the past two thousand years of experience with God and man?