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A significant challenge in today's electronic design is designing complex, high-performance, “reliable” systems out of available components that are often “unreliable”, their behavior being affected by uncertainties or stochastic fluctuations. The problem is to guide the design process towards robustness, i.e., making the design insensitive to parameter variations. In this paper, we review design techniques, methodologies and tools that address robust design in the context of analog and mixed-signal integrated systems. Our analysis is organized in two areas: architectures and methodologies with supporting tools. Design approaches based on calibration techniques have been traditionally used to tune analog performance and meet the required specifications. Digitally-assisted and system-assisted design approaches build circuits that are tolerant to impaired analog components. We survey statistical modeling and optimization techniques that are instrumental to robust, hierarchical design of complex systems. Finally, we discuss platform-based design and contract-based design as viable frameworks for robust design methodologies and tools to be developed into a structured design flow.