Intelligent biomedical devices implies systems that are able to detect specific physiological processes in patients so that particular responses can be generated. This closed-loop capability can have enormous clinical value when we consider the unprecedented modalities that are beginning to emerge for sensing and stimulating patient physiology. Both delivering therapy (e.g., deep-brain stimulation, vagus nerve stimulation, etc.) and treating impairments (e.g., neural prosthesis) requires computational devices that can make clinically relevant inferences, especially using minimally-intrusive patient signals. The key to such devices is algorithms that are based on data-driven signal modeling as well as hardware structures that are specialized to these. This paper discusses the primary application-domain challenges that must be overcome and analyzes the most promising methods for this that are emerging. We then look at how these methods are being incorporated in ultra-low-energy computational platforms and systems. The case study for this is a seizure-detection SoC that includes instrumentation and computation blocks in support of a system that exploits patient-specific modeling to achieve accurate performance for chronic detection. The SoC samples each EEG channel at a rate of 600 Hz and performs processing to derive signal features on every two second epoch, consuming 9 μJ/epoch/channel. Signal feature extraction reduces the data rate by a factor of over 40×, permitting wireless communication from the patient’s head while reducing the total power on the head by 14×