The interstellar medium (ISM) is a multi-phase, magnetized, and highly turbulent medium. In this paper, we address both theoretical and observational aspects of plasma turbulence in the ISM. We successively consider radio wave propagation through a plasma and radio polarized emission. For each, we first provide a theoretical framework in the form of a few basic equations, which enable us to define useful diagnostic tools of plasma turbulence; we then show how these tools have been utilized to detect and interpret observational signatures of plasma turbulence, and what astronomers have learned from them regarding the nature, the sources, and the dissipation of turbulence in the ISM.