Using ab initio evolutionary simulations, we predict the existence of five novel stable Li-N compounds at pressures from 0 to 100 GPa (Li13N, Li5N, Li3N2, LiN2, and LiN5). Structures of these compounds contain isolated N atoms, N2 dimers, polyacetylene-like N chains and N5 rings, respectively. The structure of Li13N consists of Li atoms and Li12N icosahedra (with N atom in the center of the Li12 icosahedron) - such icosahedra are not described by Wade-Jemmis electron counting rules and are unique. Electronic structure of Li-N compounds is found to dramatically depend on composition and pressure, making this system ideal for studying metal-insulator transitions. For example, the sequence of lowest-enthalpy structures of LiN3 shows peculiar electronic structure changes with increasing pressure: metal-insulator-metal-insulator. This work also resolves the previous controversies of theory and experiment on Li2N2.