Most existing telephone networks transmit narrowband coded speech which has been bandlimited to 4 kHz. Compared with normal speech, this speech has a muffled quality and reduced intelligibility, which is particularly noticeable in sounds such as /s/, /f/ and /sh/. Speech which has been bandlimited to 8 kHz is often coded for this reason, but this requires an increase in the bit rate. Wideband enhancement is a scheme that adds a synthesized highband signal to narrowband speech to produce a higher quality wideband speech signal. The synthesized highband signal is based entirely on information contained in the narrowband speech, and is thus achieved at zero increase in the bit rate from a coding perspective. Wideband enhancement can function as a post-processor to any narrowband telephone receiver, or alternatively it can be combined with any narrowband speech coder to produce a very low bit rate wideband speech coder. Applications include higher quality mobile, teleconferencing, and internet telephony. This thesis examines in detail each component of the wideband enhancement scheme: highband excitation synthesis, highband envelope estimation, and narrowband-highband envelope continuity. Objective and subjective test measures are formulated to assess existing and new methods for all components, and the likely limitations to the performance of wideband enhancement are also investigated. A new method for highband excitation synthesis is proposed that uses a combination of sinusoidal transform coding-based excitation and random excitation. Several new techniques for highband spectral envelope estimation are also developed. The performance of these techniques is shown to be approaching the limit likely to be achieved. Subjective tests demonstrate that wideband speech synthesized using these techniques has higher quality than the input narrowband speech. Finally, a new paradigm for very low bit rate wideband speech coding is presented in which the quality of the wideband enhancement scheme is improved further by allocating a very small bitstream for highband envelope and gain coding. Thus, this thesis demonstrates that wideband speech can be communicated at or near the bit rate of a narrowband speech coder.