Both helium and ammonia are main components of icy giant planets. While ammonia is very reactive, helium is the most inert element in the universe. It is of great interest whether ammonia and helium can react with each other under planetary conditions, and if so, what kinds of structures and states of matter can form. Here, using crystal structure prediction methods and first-principles calculations, we report 3 new stable stoichiometries and 8 new stable phases of He-NH3 compounds under pressures up to 500 GPa. These structures may exhibit perovskite-like structures for HeNH3 and He2NH3, and a host-guest crystal structure for He(NH3)2. Superionic states are found in all these He-NH3 compounds under high pressures and temperatures in which the hydrogen atoms are diffusive while the nitrogen and helium atoms remain fixed. Such 1 / 26 dynamical behavior in helium-ammonia compounds is quite different from that in helium-water compounds, where weakly interacting helium is more diffusive than stronger bound hydrogen. The low-density host-guest phase of space group I4cm is found to be stable at very low pressures (about 3 GPa) and it enters into a plastic state, characterized by freely rotating ammonia molecules. The present results suggest that plastic or superionic helium-ammonia compounds may exist under planetary conditions, and helium contributes crucially to the exotic physics and chemistry observed under extreme conditions.