Optoelectronic devices and measurement techniques now operate at speeds ranging from picoseconds to hundreds of femtoseconds, have a dynamic range that extends from microvolts to kilovolts, are virtually jitter-free, and can make measurements in a wide variety of circuits, devices, and materials without requiring direct electrical contacts to the samples under test. This tutorial summarizes recent work on this topic emphasizing the basic device and measurement concepts and the diverse uses in electronics, materials science, and communications.