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In this paper, we identify quality dimensions which are relevant for speech communication services, such as mobile telephony or Voice-over-IP. These include dimensions perceived when listening to degraded speech, talking against echoes, double-talk capabilities, interacting with delay, conversing over channels with time-varying characteristics, and service-related dimensions experienced during speech connection set-up and maintenance. For each dimension, we review subjective evaluation metrics and instrumental quality prediction models. We group these dimensions in a framework model which is able to diagnostically assess speech communication services, and may be used for monitoring and maintenance.