This is an amazing question. It assumes a lot, though. It assumes that modern history, at least in some ways, has been a search for utopia. Not all people would agree. In my opinion, we can view modern history as a search for utopia, even if it is a failed one.
First, one of the most obvious answers we can give is people in the modern world have looked to technology to create a utopia. Through technology people can communicate better, have better qualities of life, and enjoy better heath through advancements in medicine. In light of these points, many people have looked to technology to usher in a utopia. Technology has promised much, and to be fair, done much, but it did not create a utopia. It also behooves me to point out that technology has also produced much suffering for the world.
Second, many people have also viewed education and enlightenment as a way to create a utopian society. For example, if all people were educated, then there would be no more wars, conflict, poverty, and the like. Education, of course, has helped, but at times education created more sophisticated ways to discriminate. The holocaust would be an example of this.
Finally, we can look to religion, especially ecumenical movements. Many religious people in the modern world have looked to the bare essentials of religion to bring people together - the fatherhood of God and the brotherhood of man. This, too, failed, because not all religions are compatible. If anything, today we have the emergence of a new conservatism in all religions, even if we do not want to admit it.
In the end, the modern world has sought something better, a utopia, but in the end it has not succeeded. However, this does not mean that we should not persist in this noble pursuit.