Coda Wave Interferometry is an increasingly popular seismic method based on ambient noise correlation functions or seismic multiplets. Its ability to detect subtle changes in the seismic velocity and structure of a medium makes it a useful tool to complement classical approaches of monitoring volcanoes. Yet, obtaining robust results and reliable interpretations requires understanding the theoretical background and assumptions of Coda Wave Interferometry, the relevant data processing and how they relate to the physical processes that can produce perturbations within a volcano. This chapter aims at expounding basic notions in this field to volcano seismologists and observers in charge of volcano monitoring. We start with the extraction of Green functions by ambient noise correlation, the description of seismic noise sources, and the propagation of coda waves in scattering media. We then present the different techniques for calculating cross-correlation functions and detecting seismic multiplets, including the quality control procedures, as well as the main methods for estimating velocity variations and for locating the perturbations. We review the most common processes that produce these perturbations within volcanoes: stress variations, effects of hydrothermal fluids, meteorological phenomena, rock damaging and softening. Finally, we lay out some perspectives and research directions on theoretical aspects, instrumentation, data processing, applications to volcano monitoring, and physical processes that produce velocity changes and decorrelation.