The First Star
The universe is believed to be infinite in all directions. We reside within an observable universe, which is the spherical region around us that has had time for its light to reach us. This is expanding and it is called the particle horizon. As time passes, further regions have had time for their young light to reach us.
So you'd think over time we'd see more and more new light.
But there is another sphere, the Hubble Volume. This relates to the expansion of the universe. Objects beyond this range are actually receding from us at greater than the speed of light due to the expansion of space.
In an accelerating universe, which we believe ours to be, this volume will lag behind the particle horizon. What this means is that in actuality, the universe we can see is shrinking, at least in 'contents' as objects near the edge over take the Hubble Boundary. At that point, the light they emit at that time will (once it travels all the way back to earth) be the last we ever see of it. They will essentially disappear from our universe.
I believe this is already happening with the most distant possibly visible objects, although I am not certain we are actually able to see them with our technology.