The cost of speech signal processing and other computationally intensive functions is increasingly influenced by power consumption as products are made smaller and more portable. That is, in portable products, weight and battery life are bigger issues than silicon area and total computational capability. A recent emphasis on the power problem within the VLSI signal processing community has led to an understanding of how parallelism can significantly reduce the cost of a system by greatly reducing clock speed, supply voltage, and power consumption, even though at the expense of silicon area and other measures of efficiency. Several different kinds and degrees of parallelism, including massive analog parallelism, should be considered in planning to reduce the total cost of speech signal processors. In this tutorial paper, recent and older ideas are reviewed with respect to their potential applicability to modern products, as well as with respect to their difficulties.