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Slow and fast light in quantum-well (QW) and quantum-dot (QD) semiconductor optical amplifiers (SOAs) using nonlinear quantum optical effects are presented. We demonstrate electrical and optical controls of fast light using the coherent population oscillation (CPO) and four wave mixing (FWM) in the gain regime of QW SOAs. We then consider the dependence on the wavelength and modal gain of the pump in QW SOAs. To enhance the tunable photonic delay of a single QW SOA, we explore a serial cascade of multiple amplifiers. A model for the number of QW SOAs in series with variable optical attenuation is developed and matched to the experimental data. We demonstrate the scaling law and the bandwidth control by using the serial cascade of multiple QW SOAs. Experimentally, we achieve a phase change of 160° and a scaling factor of four at 1 GHz using the cascade of four QW SOAs. Finally, we investigate CPO and FWM slow and fast light of QD SOAs. The experiment shows that the bandwidth of the time delay as a function of the modulation frequency changes in the absorption and gain regimes due to the carrier-lifetime variation. The tunable phase shift in QD SOA is compared between the ground- and first excited-state transitions with different modal gains.