Currently, via the mediation of audio mining technology and conversational user interfaces, and after years of constant improvements of Automatic Speech Recognition technology, conversation intelligence is an emerging concept, significant to the understanding of human-human communication in its most natural and primitive channel – our voice. This paper introduces the concept of Conversation Intelligence (CI), which is becoming crucial to the study of humanhuman speech interaction and communication management and is part of the field of speech analytics. CI is demonstrated on two established discourse terms – power relations and convergence. Finally, this paper highlights the importance of visualization for large-scale speech analytics.