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The fields of brain‐inspired computing, robotics, and, more broadly, artificial intelligence (AI) seek to implement knowledge gleaned from the natural world into human‐designed electronics and machines. In this review, the opportunities presented by complex oxides, a class of electronic ceramic materials whose properties can be elegantly tuned by doping, electron interactions, and a variety of external stimuli near room temperature, are discussed. The review begins with a discussion of natural intelligence at the elementary level in the nervous system, followed by collective intelligence and learning at the animal colony level mediated by social interactions. An important aspect highlighted is the vast spatial and temporal scales involved in learning and memory. The focus then turns to collective phenomena, such as metal‐to‐insulator transitions (MITs), ferroelectricity, and related examples, to highlight recent demonstrations of artificial neurons, synapses, and circuits and their learning. First‐principles theoretical treatments of the electronic structure, and in situ synchrotron spectroscopy of operating devices are then discussed. The implementation of the experimental characteristics into neural networks and algorithm design is then revewed. Finally, outstanding materials challenges that require a microscopic understanding of the physical mechanisms, which will be essential for advancing the frontiers of neuromorphic computing, are highlighted.