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AlGaInP lattice matched to GaAs is suited for light-emitting diodes (LEDs) operating in the red, orange, yellow, and yellow–green wavelength range. Such long-wavelength visible-spectrum devices will play an important role in solid-state lighting applications. This review discusses the major classes of AlGaInP device structures, including absorbing-substrate (AS) LEDs, absorbing substrate LEDs enhanced by distributed-Bragg-reflectors (DBRs), transparent substrate (TS) LEDs, thin-film (TF) LEDs, and LEDs using omnidirectional reflectors (ODRs). Some of these device structures have well-known deficiencies: A significant fraction of light is absorbed in the GaAs substrate in AS-LEDs; DBRs are essentially transparent at oblique angles of incidence leading to substantial optical losses. More recent developments such as TS-LEDs and TF-LEDs avoid these drawbacks. High-reflectivity, electrically conductive ODRs were recently developed that considerably outperform conventional distributed Bragg reflectors. LEDs using such conductive ODRs can replace DBRs in AlGaInP LEDs and are potential candidates for low-cost high-efficiency LEDs suitable for high-power solid-state lighting applications. © 2004 American Institute of Physics.