The performance of current speech recognition systems is far below that of humans. Neural nets offer the potential of providing massive parallelism, adaptation, and new algorithmic approaches to problems in speech recognition. Initial studies have demonstrated that multilayer networks with time delays can provide excellent discrimination between small sets of pre-segmented difficult-to-discriminate words, consonants, and vowels. Performance for these small vocabularies has often exceeded that of more conventional approaches. Physiological front ends have provided improved recognition accuracy in noise and a cochlea filter-bank that could be used in these front ends has been implemented using micro-power analog VLSI techniques. Techniques have been developed to scale networks up in size to handle larger vocabularies, to reduce training time, and to train nets with recurrent connections. Multilayer perceptron classifiers are being integrated into conventional continuous-speech recognizers. Neural net architectures have been developed to perform the computations required by vector quantizers, static pattern classifiers, and the Viterbi decoding algorithm. Further work is necessary for large-vocabulary continuous-speech problems, to develop training algorithms that progressively build internal word models, and to develop compact VLSI neural net hardware.