Interest in acoustoelectric SAW devices has grown rapidly in the past few years. One of the reasons for this expansion is the potential capability of these devices to perform sophisticated real-time programmable signal processing. The essential ingredient in these devices is the acoustoelectric interaction of free carriers in a semiconductor with the evanescent RF electric fields accompanying surface acoustic waves (SAWs) propagating on a nearby piezoelectric substrate. Coupling of the electric fields from the piezoelectric to the semiconductor takes place across a narrow (-300 nm) air gap. The complexity of the semiconductor ranges from the simple distributed surface varactor of the convolver, to the high density diode array (few pm periodicity) of the acoustoelectric devices with charge storage, to the fully integrated microcircuit of the complex charged-coupled devices (SAW/CCD). The convolver provides, in a compact structure, matched filtering with a processing gain in excess of 30 dB and bandwidths up to 200-MHz for spread-spectrum waveforms, a function which would otherwise require a large digital machine operating at 1011 arithmetic operations per second. Other devices, newer than the convolver, are being explored which promise increasingly sophisticated signal processing capability. For instance, the memory correlator and the SAW/CCD programmable matched filter can be used in radar receivers in place of fixed matched filters to reduce the time spent in system alignment and to introduce programmability; the integrating correlator and the SAW/CCD accumulating correlator have the potential to be used in spread-spectrum systems for the correlation of very long (Ã¢â‚¬â€?msec) waveforms and the coherent integrator could provide a programmable burst-waveform processor for pulse-Doppler radar. As examples of the large variety of acoustoelectric SAW signal processors, three specific air-gap devices, the convolver, the memory correlator, and the coherent integrator will be described.