Since the universe is always expanding, that means there's an edge right? So what are some theories for outside of that growing edge.
There are a number of ways of answering this question. Here are a few.
Firstly we can simply state that, by definition, the universe is everything and therefore there is simply nothing beyond it. Not nothing as in empty space, but nothing at all, not even space (or it could be that the universe is infinite.)
Secondly, we could look at what we mean when we say that the universe is expanding. What this really means is that the space-time metric is growing. It does not mean that the universe is expanding into some void, but that distances inside the universe are increasing with time. My favourite parallel is with an balloon being blown up. Points on the surface get further away without the addition of any more material to the balloon. (It is, of course, an imperfect parallel as the balloon is expanding in a medium).
Thirdly, and now we are touching on metaphysics (in the sense that it may be impossible to test some or any of these theories), we can say that "our" universe is one of many and that, actually it may well have an edge which even now is crashing into some other universe, or perhaps we are inside a black hole inside another universe. These multiverse theories are ten-a-penny but they are not without scientific merit, possibly.
There are several theorie of what is outside of the universe. The problem with all these theories is that there is no empirical way to falsify or proof these theories and therefore have a high level of speculation and what theory you think best suites your believes. The theories can be classified into single universe theories and multiverse theories.
The single universe theories state that our universe lies in a vast / infinite universe that is much larger than what we can see now. We are limited in seeing beyond the hubble volume, since the speed of light prevents us from seeing things beyond the distance that light has travelled since our known universe started to exist. There are several theories on what lies beyond the hubble volume, which vary from nothing to dark matter structures that have a gravitational pull on the observable universe. In these theories the universe is not expanding, but the hubble volume is expanding with the age of the universe.
The multiverse universe is actually a variation of the single universe theory. It also states that there is a large vastness, however, filled with multiple universes. Either in a single universe there are bubbles of universes where each bubble is created by a big bang. The other is spun out of the string theory, which states that there are always energy ripples in a perfect vacuum, which can lead to the existence of multiple universes. The theory is here further explained. Another theory is the fecund theory, which states that each black hole in the universe spawns a new universe with slightly different physical laws.
So, to answer your question concisely. "What happens outside of the universe?" Whatever you believe.