Prime motivators in the evolution of increasingly sophisticated communication and detection systems are the needs for handling ever wider signal bandwidths and higher data processing speeds. These same needs drive the development of electronic device technology. Until recently the superconductive community has been tightly focused on digital devices for high speed computers. The purpose of this paper is to describe opportunities and challenges which exist for both analog and digital devices in a less familiar area, that of wideband signal processing. The function and purpose of analog signal-processing components, including matched filters, correlators and Fourier transformers, will be described and examples of superconductive implementations given. A canonic signal-processing system is then configured using these components in combination with analog/digital converters and digital output circuits to highlight the important issues of dynamic range, accuracy and equivalent computation rate. Superconductive circuits hold promise for processing signals of 10-GHz bandwidth. Signal processing systems, however, can be properly designed and implemented only through a synergistic combination of the talents of device physicists, circuit designers, algorithm architects and system engineers. An immediate challenge to the applied superconductivity community is to begin sharing ideas with these other researchers.