This chapter explains how exactly we are going to examine the spoken interaction in this corpus, as well as how the interaction engine is organised as a complex adaptive system. This chapter explains how we analyse instances of talk using the methodology of Conversation Analysis (CA). The basic mechanisms and concepts of CA are firstly introduced in this chapter in relation to the baseline of ordinary conversation. We see how the component mechanisms of the interaction engine combine to create an ‘architecture of intersubjectivity’ which enables people to perform an enormous range of social actions, creating a social world as they see fit; the same architecture enables us to analyse their actions. This is as a preface to showing how these mechanisms adapt themselves to mirror institutional or social goals, looking at both L2 classroom interaction and the L2 talk in our corpus. We argue that CA is able to portray how spoken interaction functions as a complex adaptive system because CA is itself a complex system which adapts itself to and mirrors the interaction which it analyses. We show in this chapter (1) how spoken interaction is organised as a complex adaptive system, (2) how CA functions as a complex adaptive system, (3) how CA can be applied to L2 talk in this informal setting, and (4) how CA relates to CDST and how they can be combined. The chapter describes the basics of how the interaction engine functions as a complex adaptive system by describing how CA works; this is possible as CA is a mirroring methodology, and we explain below what is meant by this. We use the term ‘CA-CDST approach’ to refer to our application of CA to analysing human spoken interaction as a complex adaptive system, discussed in Section 3.6.4.