Acoustically tunable narrow band optical filters are based on the phase-matched interaction of light and sound in certain crystals. With such filters, scanning in wavelength and adjustment of bandwidth can be done completely electronically, without mechanical devices. Such an approach can lead to reductions in instrument size and complexity, and facilitate incorporation of the spectrometer into computer-controlled systems. Some advantages over mechanical systems include rapid scanning, multiwavelength sampling, and fast, random access to spectral regions of interest. We review the basic interaction phenomena involved in the process. Parameters such as required acoustic power densities, bandwidths and angular apertures attainable, and the trade-offs among them are discussed. Acoustooptic filters based on presently available materials can now cover the visible and mid-infrared spectral regions. We describe the details of such systems, with emphasis on our own work in the mid-infrared. The potential of such filters for application in rapid scanning, random access and imaging spectroscopy is also discussed.