The anti-saccade task has emerged as an important tool for investigating the complex nature of voluntary behaviour. In this task, participants are instructed to suppress the natural response to look at a peripheral visual stimulus and look in the opposite direction instead. Analysis of saccadic reaction times (SRT: the time from stimulus appearance to the first saccade) and the frequency of direction errors (i.e. looking toward the stimulus) provide insight into saccade suppression mechanisms in the brain. Some direction errors are reflexive responses with very short SRTs (express latency saccades), while other direction errors are driven by automated responses and have longer SRTs. These different types of errors reveal that the anti-saccade task requires different forms of suppression, and neurophysiological experiments in macaques have revealed several potential mechanisms. At the start of an anti-saccade trial, pre-emptive top-down inhibition of saccade generating neurons in the frontal eye fields and superior colliculus must be present before the stimulus appears to prevent express latency direction errors. After the stimulus appears, voluntary anti-saccade commands must compete with, and override, automated visually initiated saccade commands to prevent longer latency direction errors. The frequencies of these types of direction errors, as well as SRTs, change throughout the lifespan and reveal time courses for development, maturation, and ageing. Additionally, patients diagnosed with a variety of neurological and/or psychiatric disorders affecting the frontal lobes and/or basal ganglia produce markedly different SRT distributions and types of direction errors, which highlight specific deficits in saccade suppression and inhibitory control. The anti-saccade task therefore provides valuable insight into the neural mechanisms of saccade suppression and is a valuable tool in a clinical setting. This article is part of the themed issue ‘Movement suppression: brain mechanisms for stopping and stillness’.