The aim of the paper is to present a theory agenda for component-based design based on results that motivated the development of the BIP component framework, to identify open problems and discuss further research directions. The focus is on proposing a semantically sound theoretical and general framework for modelling component-based systems and their properties both behavioural and architectural as well for achieving correctness by using scalable specific techniques. We discuss the problem of composing components by proposing the concept of glue as a set of stateless composition operators defined by a certain type of operational semantics rules. We provide an overview of results about glue expressiveness and minimality. We show how interactions and associated transfer of data can be described by using connectors and in particular, how dynamic connectors can be defined as an extension of static connectors. We present two approaches for achieving correctness for component-based systems. One is by compositional inference of global properties of a composite component from properties of its constituents and interaction constraints implied by composition operators. The other is by using and composing architectures that enforce specific coordination properties. Finally, we discuss recent results on architecture specification by studying two types of logics: 1) interaction logics for the specification of sets of allowed interactions; 2) configuration logics for the characterisation of architecture styles.