Rare-earth-activated nitride and oxynitride phosphors are attractive converter materials for white-LEDs applications due to their efficient luminescent characteristics, high thermal and chemical stabilities because their basic crystal structure is built on rigid tetrahedral networks, either of the Si–(O,N) or Al–(O,N) type. Recent progress in fluorescence properties of silicon–aluminum–(oxy)nitride-based luminescent materials with broad excitation bands activated by Eu2+, Ce3+, and Yb2+ for phosphor-converted white-LEDs are reviewed in this article, with the emphasis on the dependence of luminescence properties on composition. We elaborate on these composition-dependent properties in three sections: (i) Eu2+-activated nitride and oxynitride phosphors; (ii) Ce3+-activated nitride and oxynitride phosphors; and (iii) Yb2+-doped α-SiAlON phosphor. Eu2+- or Ce3+-activated nitride and oxynitride phosphors are categorized into four parts following the structural and/or composition characteristics, i.e., α-SiAlON, β-SiAlON, oxonitridosilicates, nitridoalumosilicates, and nitridosilicates. Some involving aspects for designing and the trends of research and development of these phosphors are addressed at the end of this article.