Low-bit-rate speech coding, at rates below 4 kb/s, is needed for both communication and voice storage applications. At such low rates, full encoding of the speech waveform is not possible; therefore, low-rate coders rely instead on parametric models to represent only the most perceptually relevant aspects of speech. While there are a number of different approaches for this modeling, all can be related to the basic linear model of speech production, where an excitation signal drives a vocal-tract filter. The basic properties of the speech signal and of human speech perception can explain the principles of parametric speech coding as applied in early vocoders. Current speech modeling approaches, such as mixed excitation linear prediction, sinusoidal coding, and waveform interpolation, use more-sophisticated versions of these same concepts. Modern techniques for encoding the model parameters, in particular using the theory of vector quantization, allow the encoding of the model information with very few bits per speech frame. Successful standardization of low-rate coders has enabled their widespread use for both military and satellite communications, at rates from 4 kb/s all the way down to 600 b/s. However, the goal of toll-quality low-rate coding continues to provide a research challenge.