The alpha rhythm, first identified by Hans Berger 100 years ago, is the dominant non-invasive electrophysiological signature of the healthy human brain in the awake state. For decades, it was believed that the alpha rhythm reflected rest or idling; however, this perspective changed in the 2000s when researchers found that alpha oscillations increase with cognitive demands. This discovery led to a paradigm shift, demonstrating that alpha oscillations reflect the functional inhibition of brain regions that are not needed for a specific task, thereby directing information to task-specific areas. We have reviewed the physiological mechanisms involved in generating alpha oscillations, which has informed computational models explaining how these oscillations emerge within physiologically realistic networks. At the behavioural level, alpha oscillations are strongly modulated across nearly all cognitive paradigms tested in humans, reflecting the allocation of computational resources within the active brain network. Research in individuals with attention-related issues has highlighted their impaired ability to modulate alpha oscillations, which is associated with performance deficits. Therefore, further exploration of alpha oscillations has the potential to uncover causal mechanisms underlying attention problems, such as those related to ADHD and ageing. Lastly, advancements in technology are opening new avenues for characterising alpha oscillations in ecologically valid settings and across the lifespan. This progress sets the stage for exploring the role of alpha oscillations in cognitive development and their functioning in natural environments.