At first glance, as the Universe is 13.7 billion years old, it seems natural to think that any object at a greater distance than 13.7 billion light-years will not be visible. However, as the Universe is expanding, photons in the cosmic microwave background (the first light emitted) have traveled approximately 45 billion light-years to get there: this makes the observable Universe about 90 billion light-years across.
This is the part I can't get my head around.
But the cosmic background radiation bit has also never made sense to me. If these microwaves date to the time of the Big Bang, then they all originated at a single point and all were emitted within the same narrow window of time. So how can it be "background" radiation? Shouldn't it be a thin hollow globe of radiation, like a glass Christmas ornament but made of microwaves, the size of the universe and expanding at the speed of light? And with nothing behind it, since the emissions of the Bang stopped at some point? Wouldn't you need a continuous radiator to have the radiation be distributed evenly as a "background"?