A survey of antimatter reactions is presented, including the formation of the antihydrogen atom and anionic, cationic, and molecular species by collisional and radiative processes. Our approach is rooted in the detailed knowledge available for many matter counterpart (hydrogenic) reactions, due to their importance in controlling early Universe chemistry. We point out that the availability of trapped antihydrogen at densities similar to those pertaining to the epoch of hydrogen chemistry will soon be available. In addition, using modern atomic physics techniques, it should be feasible to control antimatter in the laboratory to facilitate antihydrogen chemistry. Our purpose is to summarize what is known from hydrogen chemistry that is of relevance for antimatter and to indicate, based on possible reaction rates, which processes may be fruitful to pursue to create new antimatter entities as probes of fundamental symmetries. We include antihydrogen, positrons, and antiprotons in our discussion and additionally the electron due to its propensity to form positronium and perhaps to participate in certain reactions. We attempt to indicate whether further theoretical/computational work is necessary to add to the assessment of reaction rates, and we discount processes where the projected rates are too low to be of interest, given foreseeable experimental capabilities.