We shall develop a simple and natural formalization of the idea of client-server architectures, and, based on this, define a notion of orthogonality between clients and servers, which embodies strong correctness properties, and exposes the rich logical structure inherent in such systems. Then we generalize from pure clients and servers to components, which provide some services to the environment, and require others from it. We identify the key notion of composition of such components, in which some of the services required by one component are supplied by another. This allows complex systems to be built from ultimately simple components. We show that this has the logical form of the Cut rule, a fundamental principle of logic, and that it can be enriched with a suitable notion of behavioural types based on orthogonality, in such a way that correctness properties are preserved by composition. We also develop the basic ideas of how logical constructions can be used to develop structured interfaces for systems, with operations corresponding to logical rules. Finally, we show how the setting can be enhanced, and made more robust and expressive, by using names (as in the π-calculus) to allow clients to bind dynamically to generic instances of services.