Random vibration is the one that is not deterministic; it will generally be arbitrary and cannot be expressed as a function of time of known characteristics. Much of the vibration arising from nature falls into this category, for example, earthquake, wind loading, and turbulence, etc. This chapter discusses a general systematic approach to the study of arbitrary signals and shows that they do have a statistical regularity that easily falls into place due to frequency analysis. It provides the basis for introducing many concepts that are useful for many applications in addition to vibro-acoustics. The chapter describes the concept of broadband excitation and the driving force of many vibro-acoustic systems. Study of random vibration is closely related to the measurement and analysis of vibration and acoustic signals. Computing the auto spectrum, cross spectrum, autocorrelation, cross correlation, system transfer function, coherence, and sound intensity requires basic knowledge of random vibration.