The paper presents an overview of adaptive filter techniques as applied to the digital coding of speech. Specifically, a model of the human speech production mechanism provides a basis for modelling the speech waveform, and this is exploited to provide efficient means for its digital encoding and transmission. During recent years the expected future demand for high-grade secure mobile communications, and the necessity to conserve bandwidth, have given impetus to an already high level of research activity in this field. The basic model of speech used for analysis has been refined in a number of ways in order to effect a reduction in the required data rate while incurring only a minimal loss of speech quality. The advantages and disadvantages of the various techniques reported in the literature are discussed in the paper. In addition, methods for enhancing voice performance when acoustic noise is present at the microphone are described. This aspect is an important one for a number of applications, particularly mobile communications from moving vehicles. The paper includes sections on digital signal processing hardware developed by Racal to implement the algorithms.