Doping of calcium tantalate, Ca2Ta2O7, with small amounts (<5 mole%) of Ca2Nb2O7 results in a 50% increase in the dielectric constant, K (from 23 to 35 at 1 MHz), and a zero temperature coefficient of K is achieved at about 18 mole% of Ca2Nb2O7. This opens up the possibility of applications in microwave communication devices. Crystallographic information needed to understand the structure/property relationships in this system is lacking. We have prepared samples of calcium tantalates doped with different elements including Nb, Sm, Ti, Nd and Zr, and have structurally characterised them using X-ray diffraction and transmission electron microscopy. The diffraction patterns of the tantalates all display strong subcell reflections characteristic of the trigonal weberite structure together with complex distributions of superlattice reflections that depend on the nature and concentration of the dopant and on the reaction temperature. The diffraction patterns were indexed using related trigonal or pseudo-trigonal unit cells with a ~7.3 Å, c ~ n × 6 Å. Polytypes with n = 3, 4, 5, 6 and 7 were prepared as single crystals by the flux method. Single crystal X-ray data was used in conjunction with high resolution electron microscope images to solve the structures. Details are given for a 6M polytype (M=monoclinic). A characteristic structural feature of the polytypes is a fluorite-type cation array which is periodically twinned on (111)f to give mixed cubic-hexagonal stacking of the cation layers. The structure relations with the pyrochlore and weberite structures are discussed.