DR-BIP is an extension of the BIP component framework intended for programming reconfigurable systems encompassing various aspects of dynamism. It relies on architectural motifs to structure the architecture of a system and to coordinate its reconfiguration at runtime. An architectural motif defines a set of interacting components that evolve according to reconfiguration rules. With DR-BIP, the dynamism can be captured as the interplay of dynamic changes in three independent directions 1) the organization of interactions between instances of components in a given configuration; 2) the reconfiguration mechanisms allowing creation/deletion of components and management of their interaction according to a given architectural motif; 3) the migration of components between predefined architectural motifs which characterizes dynamic execution environments. The paper lays down the formal foundation of DR-BIP, illustrates its expressiveness on few examples and discusses avenues for dynamic reconfigurable system design.