We can define the universe as everything there is, so in that case there is nothing outside of it. We also say that space and time both started at the Big Bang and therefore there was nothing before it.
Another definition for the universe is the observable universe - which is the part of it that we can technically see. We cannot know what is outside of that (since we can't observe it), but we think that physics works the same everywhere and so we think that it should be very similar to the observable universe. We actually think that the universe might be infinite in extent, and so goes on forever, even though we can only see a finite part of it.
We can speculate in meta-physics or in religion about what was before the Big Bang, but again, we cannot use science to tell anything about it as physics as we understand it breaks down at that point.
This page was last updated June 27, 2015.