In this article, we explore neurobiological principles that could be deployed in systems requiring self-preservation, adaptive control, and contextual awareness. We start with low-level control for sensor processing and motor reflexes. We then discuss how critical it is at an intermediate level to maintain homeostasis and predict system set points. We end with a discussion at a high-level, or cognitive level, where planning and prediction can further monitor the system and optimize performance. We emphasize the information flow between these levels both from a systems neuroscience and an engineering point of view. Throughout the paper, we describe the brain systems that carry out these functions and provide examples from artificial intelligence, machine learning, and robotics that include these features. Our goal is to show how biological organisms performing self-monitoring can inspire the design of autonomous and embedded systems.