Time is a fundamental dimension of human perception, cognition and action, as the perception and cognition of temporal information is essential for everyday activities and survival. Innumerable studies have investigated the perception of time over the last 100 years, but the neural and computational bases for the processing of time remains unknown. First, we present a brief history of research and the methods used in time perception and then discuss the psychophysical approach to time, extant models of time perception, and advancing inconsistencies between each account that this review aims to bridge the gap between. Recent work has advocated a Bayesian approach to time perception. This framework has been applied to both duration and perceived timing, where prior expectations about when a stimulus might occur in the future (prior distribution) are combined with current sensory evidence (likelihood function) in order to generate the perception of temporal properties (posterior distribution). In general, these models predict that the brain uses temporal expectations to bias perception in a way that stimuli are ‘regularized’ i.e. stimuli look more like what has been seen before. Evidence for this framework has been found using human psychophysical testing (experimental methods to quantify behaviour in the perceptual system). Finally, an outlook for how these models can advance future research in temporal perception is discussed.