Does the universe ever end, i.e. what lays beyond or is there anything beyond?
To my view, the really interesting thing is that we can address this question at all...
This is really a tricky question to answer, for the following reason.
According to the most recent data (obtained by the "Planck" and "WMAP" missions), the universe that we can observe is spatially flat, and thus it has no end, namely it is infinite. As far as evolution with time goes, there are firm evidence that the universe had a beginning (the so called "big bang") which took place about 13.8 billion years ago, and the universe expanded since then. According to what we know today, the universe will continue to expand forever. So, here is the catch: since light travels at the speed of light, and no signal travels faster than light, we have no way of knowing what happens at distances larger than 13.8 billion light years. (1 light year = the distance light travels in 1 year) [More precisely, we can see a slightly smaller region, since we can only see light after it decoupled matter in the early universe, and this decoupling took some time]. The part of the universe that lies beyond this distance is outside the “observable universe”: all the measurements we can do are limited to the observable universe, which, as I wrote, is consistent with being flat. Thus, the most accurate answer, I think, is that the universe that we see is consistent with being infinite. However, we know that there are parts of the universe that we cannot see, and possibly we could never see due to the expansion of the universe, that may change this picture.
So, how come the universe could be both infinite and have a beginning? While this seem like a contradiction at first, it isn't really. Simply, at the time of the big bang, the density of the universe was infinite. A simple analogue is to take a paper and put it in a copy machine, reducing the size of the copied paper. Looking at the copies paper, all the information is still there, but the letters are smaller, and everything is denser. Closer and closer to the "big bang", a very similar thing happened to our universe.
Another important point to note in this respect, is that the universe expansion is not like "normal" expansion. When we think of expansion (e.g., inflating a balloon), the object expands into a pre-existing space. Thus, it makes sense to ask what lies beyond the expanded object. However, the expansion of the universe is different. The universe was (and is) "inflated", in the sense that the distance between any two particles / atoms increases with time, while the universe is kept infinite (presumably). This is the origin of the cosmological "redshift" effect seen when looking at distant galaxies: the size of the universe at the time in which light was emitted from distant galaxies was smaller than its size today, when we observe this light. Thus, light, which is a wave, was "stretched", which causes it to look red.(and indeed, the existence of redshift is one of the observational proofs - but not the only one - for the "big bang" theory that predicts the expansion of the universe).
Thus, there is no "need" for anything to be beyond the universe.