Component-based software emerged as a promising paradigm to deal with the ever increasing need for mastering systems' complexity, for enabling evolution and reuse, and for driving software engineering into sound production and engineering standards. Soon, however, it became a popular technology long before well understood and widely adopted formal foundations have emerged. Issues like mathematical models for components, their interaction and composition, or rigorous approaches to verification, deployment, testing and certification remain open research questions and challenging opportunities for formal methods. Moreover, new challenges are raised by applications of this paradigm to safety-critical, mobile, or reconfigurable systems.