Even though corpora have transformed language education, the majority of corpus-related research focuses on the teaching of writing. Via a systematic review of previous studies and a survey of language corpora available, this study aims to ascertain whether and to what extent the teaching of speaking, especially of conversation skills, to EFL learners, has been informed by existing language corpora, to identify spoken English corpora available and discover whether they have been informed by insights from such an approach to studying conversation as Conversation Analysis (CA). Finally, the study suggests possibilities for incorporating CA insights such that CA-informed, corpus-driven language pedagogy can be materialized. Previous studies on the use of corpora for teaching speaking were examined and spoken language corpora available were identified along with how they have been recommended and applied to the teaching of speaking, as well as possibilities for developing CA-informed corpora of spoken English for conversation teaching. The study revealed that conversation teaching in the EFL context remains to be informed by corpus linguistics. Accessible spoken English corpora are not yet geared towards language teachers and learners, and there remain issues to be resolved before employing the available corpus data and confirming its efficacy in teaching EFL conversation or speaking in general.