We talked about the antiparticles, which form antimatter atoms when combined in the same way as regular particles and regular atoms. Hydrogen atoms are one electron orbiting one proton. Antihydrogen is one positron orbiting one antiproton.

Antihydrogen was produced at CERN in 1995. This was done by making antiprotons using a particle accelerator and shooting them into xenon clusters (a bunch of xenon atoms). Only a very small number of antihydrogen atoms can be made this way.

Theoretically, there would be a lot of antimatter in the universe, and therefore a lot of antihydrogen floating out there in space. This could result in higher antimatter atoms (helium, lithium, etc), and even antimatter stars and planets. This appears not to be the case, or at least it cannot be detected if it is. 

Antihydrogen? I will definitely be looking more into this. Antimatter stars and planets sounds like an awesome topic for a sci-fi work.