During the second century CE, there was a popular new religion called Manichaeism (if you've read the Church Fathers, you've heard of them). Manichaean cosmology teaches that the universe was once made up of light and darkness, light abandoned the universe, and darkness remained.
The current prevailing cosmology, with respect to antimatter, is sort of like that: at the beginning of the universe, at the Big Bang, there was both matter and antimatter. They exploded, and the vast majority of the physical universe we know is, as Michio Kaku puts it here, "the leftovers":
If antimatter sounds a little too mystical to be plausible, now would be a good time to mention that we can actually find the stuff. The Conseil Européen pour la Recherche Nucléaire (CERN) laboratory in Geneva, Switzerland can pluck individual atoms of anti-hydrogen at a rate of one every fifteen minutes or so and gather them up for testing. And one of the tests we're going to perform on them is pretty simple: we're going to determine the gravitational mass of antimatter. To put it another way, we're going to see whether antimatter falls down or falls up.
And while that sounds a bit silly, it brings us a little closer to figuring out exactly how gravity works. Besides, it wouldn't hurt to know the gravitational mass of what may have once been a commonplace type of subatomic particle—seeing as how this may give us some clue as to where the rest of it went.