Atoms made of a particle and an antiparticle are unstable, usually surviving less than a microsecond. Antihydrogen, the bound state of an antiproton and a positron, is made entirely of antiparticles and is believed to be stable. It is this longevity that holds the promise of precision studies of matter-antimatter symmetry. I will give an overview of the ALPHA experiment (with an emphasis on the physical processes involved in the measurements) which has succeeded in trapping antihydrogen in a cryogenic Penning trap for times up to 15 minutes and has successfully performed precision measurements of several properties of antihydrogen. For example, we have measured the 1S-2S frequency to about one part in a trillion. I will conclude with prospects for future precision measurements.