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Amorphous Li-ion conductors are important solid-state electrolytes. However, Li transport in these systems is much less understood than for crystalline materials. We investigate amorphous LiPON electrolytes via ab initio molecular dynamics, providing atomistic-level insight into the mechanisms underlying the Li+ mobility. We find that the latter is strongly influenced by the chemistry and connectivity of phosphate polyanions near Li+. Amorphization generates edge-sharing polyhedral connections between Li(O,N)4 and P(O,N)4, and creates under- and overcoordinated Li sites, which destabilizes the Li+ and enhances their mobility. N substitution for O favors conductivity in two ways: (1) excess Li accompanying 1(N):1(O) substitutions introduces extra carriers; (2) energetically favored N-bridging substitutions condense phosphate units and densify the structure, which, counterintuitively, corresponds to higher Li+ mobility. Finally, bridging N is not only less electronegative than O but also engaged in strong covalent bonds with P. This weakens interactions with neighboring Li+ smoothing the way for their migration. When condensation of PO4 polyhedra leads to the formation of isolated O anions, the Li+ mobility is reduced, highlighting the importance of oxygen partial pressure control during synthesis. This detailed understanding of the structural mechanisms affecting Li+ mobility is the key for optimizing the conductivity of LiPON and other amorphous Li-ion conductors.