Spontaneous speech is often impromptu and unscripted. Prescriptive speech is usually planned and rehearsed. These two modes of human communication, however similar, are set apart by nuances and characteristic features that pose significant challenges for AI systems. This chapter presents real-world examples of spontaneous human dialogues and describes in detail various artifacts present in spontaneous speech at all levels: audio, speech, and dialogue. Another defining feature of human conversations is their implicit structure consisting of dialogue acts and speaker turns. Understanding these linguistic expressions is necessary to capture the dynamics of spontaneous human dialogues. Achieving true spoken language understanding requires carefully crafted synergy between artificial intelligence and linguistics, which, in turn, is conditioned on comprehensive modeling of spontaneous human conversations.