In dissociative recombination, the kinetic energy of the incident electron is transferred into excitation of the electrons of the target ion and then into kinetic energy of the fragments. In general, this proceeds via a resonance where the electron is temporarily trapped by the ion, leading to efficient energy transfer. The study of dissociative recombination is the study of these resonances, Rydberg states converging to the ground and excited states of the ion. For a number of systems, we have studied the electronic states involved in dissociative recombination, including the ground and excited states of the ion, the resonant states and the bound Rydberg states of the system, by combining electron scattering calculations with multi-reference configuration interaction quantum chemistry calculations. We will report on trends and patterns in these resonance states. We will discuss studies of dissociative recombination of the rare-gas ions, moving down the periodic table from He⁺₂ to Ne⁺₂ to Ar⁺₂, where the ground electronic state of the ion is constant, but its polarizability increases. We will also present results on isoelectronic polyatomic systems, such as HCO⁺ and HCNH⁺, as well as the effects of changing the electronic structure slightly such as HCN⁺/HNC⁺ and H₂CO⁺.