We outline the role and benefits that conversations could bring to Web services in general and their composition in particular. A Web service is an accessible application that other applications and humans as well can discover and trigger to satisfy multiple needs (e.g., accommodation booking). While much of the work on Web services to date has focussed on low-level standards for publishing, discovering, and invoking Web services, it is deemed appropriate to start leveraging the Web services to the level of active components. These components would be able to engage in conversations, make decisions, and adjust their behavior according to the situations in which they participate. A conversation is a consistent exchange of messages between participants involved in joint operations and thus, have common interests.