<p>Human and animal electrophysiology often looks noisy and unstructured. While some clearer features exist in the form of bursty oscillations and event-related potentials, recent methodological developments have helped to uncover surprising structure in what otherwise looks like noise. This signal, referred to as aperiodic activity, has received substantial recent attention, examining its physiological generators and relationship to behaviour, cognition, development, ageing and disease. Here we examine the putative physiological basis of aperiodic activity, its relationship to other measures of neural activity and evidence for its functional and clinical relevance. Computational modelling and empirical evidence show that aperiodic activity has many neural origins, primarily postsynaptic transmembrane currents across populations of neurons. While several other signal statistics capture features similar to aperiodic measures, new methods have allowed researchers to more directly link aperiodic activity to underlying physiological processes. We discuss the implications of these findings for our understanding of cognition and disease, and highlight open questions for future research.</p>