The past decade has witnessed substantial progress towards the application of low-rate speech coders to civilian and military communications as well as computer-related voice applications. Central to this progress has been the development of new speech coders capable of producing high-quality speech at low data rates. Most of these coders incorporate mechanisms to: represent the spectral properties of speech, provide for speech waveform matching, and "optimize" the coder's performance for the human ear. A number of these coders have already been adopted in national and international cellular telephony standards. The objective of this paper is to provide a tutorial overview of speech coding methodologies with emphasis on those algorithms that are part of the recent low-rate standards for cellular communications. Although the emphasis is on the new low-rate coders, we attempt to provide a comprehensive survey by covering some of the traditional methodologies as well. We feel that this approach will not only point out key references but will also provide valuable background to the beginner. The paper starts with a historical perspective and continues with a brief discussion on the speech properties and performance measures. We then proceed with descriptions of waveform coders, sinusoidal transform coders, linear predictive vocoders, and analysis-by-synthesis linear predictive coders. Finally, we present concluding remarks followed by a discussion of opportunities for future research. >