Two perovskite-derived materials, CaCu3Mn4O12, have drawn much recent interest due to their magnetoresistive, dielectric, and mafnetoelectronic characteristics. Here we present initial theoretical insights into each of these points, based on first principles, density functional based calculations. Our results predict CCMO to have a spin-asymmetric energy gap, which leads to distinct temperature- and magnetic field-dependent changes in properties, and helps to account for its observed negative magnetoresistivity. We have studied CCTO primarily to gain insight into the exchange coupling in both these compounds, where the conventional superexchange coupling vanishes by symmetry for both nearest and next nearest Cu-Cu neighbors, a consequence of the structure. In CCTO, it is necessary to go 5th Cu-Cu neighbors to obstain a (superexchange) coupling that can provide the coupling necessary to give three dimensional order. Non-superexchange mechanisms may be necessary to describe the magnetic coupling in this structural clss.