Perceptual decision making is the act of choosing one option or course of action from a set of alternatives on the basis of available sensory evidence. Thus, when we make such decisions, sensory information must be interpreted and translated into behaviour. Neurophysiological work in monkeys performing sensory discriminations, combined with computational modelling, has paved the way for neuroimaging studies that are aimed at understanding decision-related processes in the human brain. Here we review findings from human neuroimaging studies in conjunction with data analysis methods that can directly link decisions and signals in the human brain on a trial-by-trial basis. This leads to a new view about the neural basis of human perceptual decision-making processes.