The EPiCS project aims at laying the foundation for engineering the novel class of proprioceptive computing systems. Proprioceptive computing systems collect and maintain information about their state and progress, which enables self-awareness by reasoning about their behaviour, and self-expression by effectively and autonomously adapt their behaviour to changing conditions. Concepts of self-awareness and self-expression are new to the domains of computing and networking; the successful transfer and development of these concepts will help create future heterogeneous and distributed systems capable of efficiently responding to a multitude of requirements with respect to functionality and flexibility, performance, resource usage and costs, reliability and safety, and security. Innovations from EPiCS are based on systematic integration of research in concepts and foundations for self-aware and self-expressive systems with novel hardware/software platform technologies and architectures for engineering autonomic compute nodes and networks. EPiCS drives and validates the research by the requirements of three challenging application domains that cover both high-end computers and embedded systems, as well as embeddings into technical and non-technical contexts.