In this talk, we present Reo, a paradigm for composition of software components based on the notion of mobile channels. Both components and channels are mobile in Reo, in the sense that (1) components can move at any time from one location to another, retaining their existing channel links, and (2) the same channels can be disconnected and reconnected to other components, thus dynamically changing the topology of inter-component communication. The component composition paradigm of Reo is in the style of the IWIM coordination model, and is an extension of our earlier work on a formal-logic-based component interface description language to convey the observable semantics of components. The main focus of attention in Reo is the channels and operations on them, not the processes that operate on them or the components they are connected to. The composition operations in Reo combine various channel types to produce complex dynamic topologies of ``connectors'' to which processes or components can be attached.