Autonomic computing (AC) is an intelligent computing approach that autonomously carries out robotic and interactive applications based on goal- and inference-driven mechanisms. This article attempts to explore the theoretical foundations and technical paradigms of AC. It reviews the historical development that leads to the transition from imperative computing to AC. It surveys transdisciplinary theoretical foundations for AC such as those of behaviorism, cognitive informatics, denotational mathematics, and intelligent science. On the basis of this work, a coherent framework toward AC may be established for both interdisciplinary theories and application paradigms, which will result in the development of new generation computing architectures and novel information processing systems.