Pyrochlore dielectric materials such as (Bi 1.5Zn 0.5)(Nb 1.5Zn 0.5)O 7 (BZN) have generated interest because they combine high dielectric constants with small dielectric loss tangents and yet are cubic at all temperatures. The recent low-temperature preparation and structural characterization of Bi 2Ti 2O 7, which remains cubic down to 2 K, has provided a good model system for understanding the properties of Bi-based pyrochlores. In this contribution, the electronic structure of cubic Bi 2Ti 2O 7 is visualized and compared with the electronic structure of the Aurivillius phase ferroelectric SrBi 2Ta 2O 9 (SBT), which displays a ferroelectric distortion below 608 K associated with the tendency of lone pair active Bi 3+ to move off-center. Such coherent off-centering distortions are frustrated on the pyrochlore lattice, and this prevents a ferroelectric-paraelectric phase transition in Bi 2Ti 2O 7. Instead, Bi 3+ ions in Bi 2Ti 2O 7 are obliged to off-center in an incoherent manner, that is compatible with the cubic structure being retained. Frustrated lone pair behavior in the defect pyrochlore Pb 2Sn 2O 6 is also described. Parallels between the well-studied frustration of certain types of magnetism in pyrochlore compounds (spin-ice) and the striking paucity of ferroelectric pyrochlores, arising from the corner-connected tetrahedral topology of the pyrochlore lattice are pointed out.