This is a rather nice, short summary on the study of anti-atoms, and in particular, CERN's effort to study the properties of anti-hydrogen and why it is so important.
With a big enough sample of anti-hydrogen, one can make detailed studies of the energy levels that the positron can occupy in its journey around the antiproton. These energy levels have been measured very precisely for hydrogen, and the expectation is that they should be identical in antihydrogen. But we won't know until we look.
The symmetry principle which these experiments are designed to test is whether physics, and therefore the whole universe, would look the same if we simultaneously swapped all matter for antimatter, left for right, and backwards in time for forwards in time. This is called a CPT (Charge/Parity/Time) inversion. The Standard Model of physics, and almost all variants on it, require that indeed the universe would be identical after such an inversion.
Now pay attention, kids. In physics, even when some of our most cherished theories have been used, and known to be valid, we STILL go out and test out many of its predictions. Here, the Standard Model says that antihydrogen should behave the same way as hydrogen. While the Standard Model certainly has been useful, and has been correct in many aspects, we do not simply accept its predictions for the behavior of antihydrogen. We still want to test it! In fact, many physicists are hoping that we see something the Standard Model can't explain, that something "weird" is going on that might give hints of new physics. This is what many of us in this field look gleefully for!
This is how science works. We verify an idea, a theory, etc., but we continue to test its RANGE OF VALIDITY, i.e. how far out does this thing work? It works here, but does it work there? It works when you do this, but does it work when you do that? This is how we expand the boundaries of our knowledge.
See how it says positronium can be regarded as a sort of light hydrogen atom? Positronium is neither matter nor antimatter. It's both. And so is hydrogen. How's that for expanding the boundaries of your knowledge?