Telephone systems commonly transmit narrowband (NB) speech with an audio bandwidth limited to the traditional telephone band of 300-3400 Hz. To improve the quality and intelligibility of speech degraded by narrow bandwidth, researchers have tried to standardize the telephonic networks by introducing wideband (50-7000 Hz) speech codecs. Wideband (WB) speech transmission requires the transmission network and terminal devices at both ends to be upgraded to the wideband that turns out to be time-consuming. In this situation, novel Bandwidth extension (BWE) techniques have been developed to overcome the limitations of NB speech. This paper discusses the basic principles, realization, and applications of BWE. Challenges and limitations of BWE are also addressed.