Polycrystalline pyrochlore oxides consisting of selected f elements (lanthanides and actinides) and Zr and Hf have been prepared and characterized. Characterization to date has been primarily by X-ray diffraction, both at room and at elevated temperatures. Initial studies concentrated on selected lanthanides and the Np, Pu and Am analogs (reported here) but have been extended to the other actinide elements through Cf. Data from these studies have been used to establish a systematic correlation regarding the fundamental materials science of these particular pyrochlores and structurally related fluorite-type dioxides. In addition to pursuing their materials science, we have addressed some potential technological applications for these materials. Some of the latter concern: (1) immobilization matrices; (2) materials for transmutation concepts; and (3) special nuclear fuel forms that can minimize the generation of nuclear wastes. For f elements that display both a III and IV oxidation state in oxide matrices, the synthetic path required for producing the desired pyrochlore oxide is dictated by their pseudo-oxidation potential the stability of the compound towards oxygen uptake. For the f elements that display an oxidationreduction cycle for pyrochlore-dioxide solid solution, X-ray diffraction can be used to identify the composition in the oxidation-reduction cycle, the oxygen stoichiometry and/or the composition. This paper concentrates on the Np, Pu and Am systems, and addresses the above aspects, the role of the crystal matrix in controlling the ceramic products as well as discussingsome custom-tailored materials.