The discovery of novel phosphors is key to the development of highly efficient and environmental friendly light-emitting diodes (LED)-based solid-state lighting. This discovery, however, has largely taken place through painstaking experiments in an Edisonian fashion. In this thesis, we use first-principles calculations to explore new phosphor materials and advance our understanding of photoluminescence (PL) properties. Phosphors with narrow-band emission are a critical component for high brightness LEDs and liquid crystal display (LCD) backlighting with wide color gamut. In the first part, we discovered a quantitative descriptor for narrow-band Eu2+-activated emission by comparing electronic structures of known narrow-band and broad-band phosphors. Incorporating this descriptor into a high throughput first principles screening of 2,259 nitride compounds, we identified five promising new nitride hosts for Eu2+-activated red-emitting phosphors that are predicted to exhibit good chemical stability, thermal quenching resistance and quantum efficiency, as well as narrow-band emission. In the second part, we performed a systematic investigation of structure-composition-property relationships in Eu2+-activated [beta]-SiAlON, one of the most promising narrow-band green phosphors. Using first-principles calculations, we first identified the most energetically favorable structure for [beta]-SiAlON:Eu2+ and then studied the effect of oxygen content and Eu2+ activator concentrations on the local EuN9 activator environment, and its impact on important PL properties such as emission peak position, bandwidth, and thermal quenching resistance. The insights obtained provide a constructive means to optimize the PL performance of [beta]-SiAlON in experiment. In the third part, we developed an approach to discover new oxide phosphors by mining unexplored chemistries with data-driven structure prediction and high-throughput screening. This approach was demonstrated by the prediction and experimental validation of a novel, earth-abundant Eu2+ and Ce3+-activated Sr2LiAlO4 phosphors. The Sr2LiAlO4:Eu2+/Ce3+ phosphors exhibit broad emissions at [lambda]max ~ 512 nm (green-yellow) and [lambda]max ~ 434 nm (blue), respectively, with excellent thermal quenching resistance of > 88% intensity at 150 C. A prototype white LED utilizing Sr2LiAlO4-based phosphors yields an excellent color rendering index exceeding 90.