A primary reason for making measurements with antimatter is to try to find clues to one of the central mysteries of our time - namely, "Where is all the antimatter?" That is, in the Big Bang, matter and antimatter were created in equal amounts but the universe is now dominated by matter. This is a good thing as matter and antimatter annihilate each other so we wouldn't be around if this wasn't the case. But it still begs the question as to the mechanism that led to the disappearance of the primordial antimatter. You can hear me talk about this on the "Big Questions" Quirks & Quarks show broadcast June 21, 2014 as well as my "the star spot" podcast Where Have All the Antimatter Gone? broadcast on June 15, 2014. A few years ago I also gave a public lecture about this using as a central theme the movie "Angels & Demons" where antimatter is used as bomb (trailer alert: not possible, so relax). By the way, while there isn't a lot of it, it is still true that there is antimatter all around us - even coming from you ... and bananas! A nice discussion of antimatter is given in Ten things you might not know about antimatter (April, 2015) although, come on, admit it, you know at least 5 of them.
I am also involved with the efforts to use trapped antihydrogen to test the
gravitational interaction between matter and antimatter (so-called "antigravity").
I wrote a little paper in 2012 -
"Why We Already Know that
Antihydrogen is Almost Certainly NOT Going to Fall "Up"" -
where I argued that it is probably
not much different from the matter-matter gravitational interaction but there is
still wiggle room and, as always, it is an experimental question! ALPHA published a
first, very imprecise limit
on the difference in 2013. We are presently designing an optimized experiment (ALPHA-g)
to probe this fundamental question.