This paper reviews the recent progress of quantum-dot semiconductor optical amplifiers developed as ultrawideband polarization-insensitive high-power amplifiers, high-speed signal regenerators, and wideband wavelength converters. A semiconductor optical amplifier having a gain of > 25 dB, noise figure of 20 dBm, over the record widest bandwidth of 90 nm among all kinds of optical amplifiers, and also having a penalty-free output power of 23 dBm, the record highest among all the semiconductor optical amplifiers, was realized by using quantum dots. By utilizing isotropically shaped quantum dots, the TM gain, which is absent in the standard Stranski-Krastanow QDs, has been drastically enhanced, and nearly polarization-insensitive SOAs have been realized for the first time. With an ultrafast gain response unique to quantum dots, an optical regenerator having receiver-sensitivity improving capability of 4 dB at a BER of 10-9 and operating speed of > 40 Gb/s has been successfully realized with an SOA chip. This performance achieved together with simplicity of structure suggests a potential for low-cost realization of regenerative transmission systems.