The realization of complex, cyber-physical "systems of systems" can substantially benefit from model-based hierarchical and compositional methodologies to make their design possible let alone optimal. In this paper, we introduce the methodology being developed within the industrial Cyber-Physical (iCyPhy) research consortium, which addresses the complexity and heterogeneity of cyber-physical systems by formalizing the design process in a hierarchical and compositional way, and provides a unifying framework where different modeling, analysis and synthesis tools can seamlessly interconnect. We use assume-guarantee contracts and their algebra (e.g. composition, conjunction, refinement) to provide formal support to the entire design flow. The design is carried out as a sequence of refinement steps from a high-level specification (top-down phase) to an implementation built out of a library of components at the lower level (bottom-up phase). At each step, the design is refined by combining synthesis from requirements, optimization and simulation-based design space exploration methods. We illustrate our approach on design examples of embedded controllers for aircraft power distribution and air management systems. 6 the application of feedback and control to networked systems, with applications in biology and autonomy. Current projects include analysis and design of biomolecular feedback circuits; specification, design and synthesis of networked control systems; and novel architectures for control using slow computing.