What lies beyond the universe?
Nothing, at least as far as we know.
The most distant reaches of the visible universe, the known universe, sit some 45 billion light years away. They are early constellations and stars. Problematic to that is the fact that they are moving away from us and that motion is accelerating. This 45 billion light years away is in all directions possible from our galaxy.
But you have to consider that we live in a universe that is approximately 13.8 billion years old and accept the fact that nothing can travel faster than the speed of light. That should mean that we cannot see anything more than 13.8 billion light years away.
Astro-physicists have explained this with the theory that in the first few seconds of its existence, the universe expanded to about one half the size it is today. That means by default the original expansion of the universe happened at a speed far greater than the speed of light to go from zero to 31 billion light years in size in a matter of seconds.
But could there be more galaxies beyond the 45 billion light years we know of? Yes!
Our ability to "see" these great distances and calculate how far away the most distant objects are rely upon our understanding of the red shift and the accuracy of the instruments we using in measuring these distances. We are in the literal infancy of such discovery.
There also exists the theory of the "multi-verse." In this theory there are an infinite number of universes and ours is simply one. Confounded to those who would like to deny such a possibility is the fact that the math supports the theory.