A computational study of the dynamic behavior of several models describing coupled oscillatory chemical reactors is presented. Special emphasis is placed on the identification of bifurcations and dynamic features that are qualitatively common in large classes of such systems. We investigate the effects of systematically varying two parameters: (a) the strength of the coupling between the two reactors, and (b) the difference between the "natural" states of the systems when they are uncoupled. For reactors which naturally oscillate, an interesting scenario involving quasiperiodicity and resonance is observed. This resembles the behavior observed in periodically forced oscillators. Indeed, the entire structure of resonance regions, and the breaking of quasiperiodic solutions as the coupling strength increases, appears to be a common feature of coupled reacting systems and coupled oscillators in general. A two-parameter computational study of the phenomenon of mutual extinction of the oscillations, which has been theoretically predicted, is also presented. The examples studied include chemical reactions in both isothermal and nonisothermal coupled CSTRs as well as a microbial predator-prey interaction in coupled isothermal chemostats.