Dynamic architectures in which interactions between components can evolve during execution, are essential for modern computing systems such as web-based systems, reconfigurable middleware, wireless sensor networks and fault-tolerant systems. Currently, we lack rigorous frameworks for their modeling, development and implementation. We propose Dy-BIP a dynamic extension of the BIP component framework rooted in rigorous operational semantics and supporting a powerful and high-level set of primitives for describing dynamic interactions. These are expressed as symbolic constraints offered by interacting components and computed efficiently by an execution Engine. We present experimental results which validate the effectiveness of Dy-BIP and show significant advantages over using static architecture models.