Compact, three-dimensional cage compounds containing optimum numbers of nitro groups as determined in theory by thermohydrodynamic calculations, constitute a class of explosive compounds more powerful than HMX. This is a direct result of high crystal densities, particularly in combination with high strain energies built into certain of the cage systems. The synthesis of polynitro cage compounds has progressed on several fronts, and is currently in the second stage of a three-stage effort. The first stage has seen the synthesis of forerunners of more highly nitrated cage compounds, as part of a broad strategy to develop the methodology for achieving the polynitration of cage molecules. The nitro cage compounds whose syntheses are in progress (second stage) and will be completed in the near future are expected to be energetic. These compounds, in turn, are expected to lead, in the third stage, to stil more highly nitrated cage compounds including those which will be signifficantly more powerful than HMX. The results of the synthesis effort to date are outlined, and achievements highlighted. In adition, the results of the calculations identifying the optium polynitro cage compounds are discussed. The future direction of the program of synthesis is indicated.