Experiences of animal and human beings are structured by the continuity of space and time coupled with the unidirectionality of time. In addition to its pivotal position in spatial processing and navigation, the hippocampal system also plays a central, multiform role in several types of temporal processing. These include timing and sequence learning, at scales ranging from meso-scales of seconds to macro-scales of minutes, hours, days and beyond, encompassing the classical functions of short term memory, working memory, long term memory, and episodic memories (comprised of information about when, what, and where). This review article highlights the principal findings and behavioral contexts of experiments in rats showing: 1) timing: tracking time during delays by hippocampal ‘time cells’ and during free behavior by hippocampal-afferent lateral entorhinal cortex ramping cells; 2) ‘online’ sequence processing: activity coding sequences of events during active behavior; 3) ‘off-line’ sequence replay: during quiescence or sleep, orderly reactivation of neuronal assemblies coding awake sequences. Studies in humans show neurophysiological correlates of episodic memory comparable to awake replay. Neural mechanisms are discussed, including ion channel properties, plateau and ramping potentials, oscillations of excitation and inhibition of population activity, bursts of high amplitude discharges (sharp wave ripples), as well as short and long term synaptic modifications among and within cell assemblies. Specifically conceived neural network models will suggest processes supporting the emergence of scalar properties (Weber’s law), and include different classes of feedforward and recurrent network models, with intrinsic hippocampal coding for ‘transitions’ (sequencing of events or places).