The goal of any speech service is the transmission and/or processing of speech signals. In this chapter we discuss the Quality of Experience (QoE) of speech communication systems, including networks, speech processing applications and terminals. We then give an overview of the methods employed to quantify and further estimate the QoE of speech communication services with a focus on diagnostic instrumental models. Such models provide indications on either the technical causes of degradations or the quality features impacted by a component in the speech communication system.