Is There an Edge to the Universe?

It is commonly theorized that the universe began with the Big Bang 13.7 billion years ago. But since we can only see as far as light has traveled in that time, we can't actually make out the edge of the universe. Could it be that the universe is infinite? Is there any way to find out what the shape of the universe really is? Can we find the edge, discover what might lie beyond it, and perhaps even discover a universe next to ours?