The dynamics of oscillatory flames is relevant to acoustically coupled combustion instabilities arising in many practical engineering systems. This paper reviews fundamental studies that pertain to the combustion of single liquid fuel droplets in an acoustically resonant environment. This flow field is not only an idealized model for the study of the fundamental interaction of reactive, evaporative, acoustic, and other transport-based timescales, but it may also be used to identify relevant phenomena in more complex or practical geometries that require a focus for future combustion control efforts. The nature of these phenomena is discussed in detail, in addition to their implications for broader issues associated with combustion instabilities.