Conversations are a well-known concept in service design to describe complex interactions between a client and one or multiple services. The REST architectural style constrains the characteristics of clients, servers and their interactions in REST architectures which consequently has an impact on conversations in such systems. The relation between conversations and REST architectures and how such RESTful conversations can be characterized has not been studied in detail yet. In this paper we discuss the characteristics of conversations in REST architectures and introduce an initial set of commonly used conversation types. Based on this, we propose to use conversations as a modeling tool for the design of REST APIs at a higher level of abstraction. We also introduce a corresponding interaction centric metamodel for REST APIs. The characterization of RESTful conversations enables a new interaction centric viewpoint on REST architectures which can be also applied for modeling REST APIs on an abstraction level that enables users to focus on the essential functionality of their REST API.