High-nitrogen-content energetic compounds containing multiple N-N bonds are an attractive alternative towards developing new generation of environmentally friendly, and more powerful energetic materials. High-N content translates into much higher heat of formation resulting in much larger energy output, detonation pressure and velocity upon conversion to large amounts of non-toxic, strongly bonded N2 gas. This thesis describes recent advances in the computational discovery of group-I alkali and hydrogen polynitrogen materials at high pressures using powerful first-principles evolutionary crystal structure prediction methods. This is highlighted by the discovery of a new family of materials that consist of long-sought after all-nitrogen N-- 5 anion and metal or hydrogen cations. The work has inspired a resurgence in the efforts to synthesize the N--5 anion. After describing the methodology of first-principles crystal structure prediction, several new high-nitrogen-content energetic compounds are described. In addition to providing information on structure and chemical composition, theory/simulations also suggests specific precursors, and experimental conditions that are required for experimental synthesis of high-N pentazolate EMs. To aid in experimenta detection of newly synthesized compounds, XRD patterns and corresponding Raman spectra are calculated for several candidate structures. The ultimate success was achieved in joint theoretical and experimental discovery of cesium pentazolate, which was synthesized by compressing and heating cesium azide CsN3 and N2 precursors in a diamond anvil cell. This success highlights the key role of first-principles structure prediction simulations in guiding experimental exploration of new high-N energetic materials.