Tephrochronology (from tephra, Gk 'ashes') is a unique stratigraphic method for linking, dating, and synchronizing geological, palaeoenvironmental, or archaeological sequences or events. As well as utilizing the Law of Superposition. tephrochronology in practise requires tephra deposits to be characterized (or 'fingerprinted') using physical properties evident in the field together with those obtained from laboratory analyses. Such analyses include mineralogical examination (petrography) or geochemical analysis of glass shards or crystals using an electron microprobe or other analytical tools including laser-ablation-based mass spectrometry or the ion microprobe. The palaeoenvironmental or archaeological context in which a tephra occurs may also be useful for correlational purposes. Tephrochronology provides greatest utility when a numerical age obtained for a tephra or cryptotephra is transferrable from one site to another using stratigraphy and by comparing and matching inherent compositional features of the deposits with a high degree of likelihood. Used this way, tephrochronology is an age-equivalent dating method that provides an exceptionally precise volcanic-event stratigraphy. Such age transfers are valid because the primary tephra deposits from an eruption essentially have the same short-lived age everywhere they occur, forming isochrons very soon after the eruption (normally within a year). As well as providing isochrons for palaeoenvironmental and archaeological reconstructions, tephras through their geochemical analysis allow insight into volcanic and magmatic processes, and provide a comprehensive record of explosive volcanism and recurrence rates in the Quaternary (or earlier) that can be used to establish time-space relationships of relevance to volcanic hazard analysis. The basis and application of tephrochronology as a central stratigraphic and geochronological tool for Quaternary studies are presented and discussed in this review. Topics covered include principles of tephrochronology, defining isochrons, tephra nomenclature, mapping and correlating tephras from proximal to distal locations at metre- through to sub-millimetre-scale, cryptotephras, mineralogical and geochemical fingerprinting methods, numerical and statistical correlation techniques, and developments and applications in dating including the use of flexible depositional age-modelling techniques based on Bayesian statistics. Along with reference to wide-ranging examples and the identification of important recent advances in tephrochronology, such as the development of new geo-analytical approaches that enable individual small glass shards to be analysed near-routinely for major, trace, and rare-earth elements, potential problems such as miscorrelation, erroneous-age transfer, and tephra reworking and taphonomy (especially relating to cryptotephras) are also examined. Some of the challenges for future tephrochronological studies include refining geochemical analytical methods further, improving understanding of cryptotephra distribution and preservation patterns, improving age modelling including via new or enhanced radiometric or incremental techniques and Bayesian-derived models, evaluating and quantifying uncertainty in tephrochronology to a greater degree than at present, constructing comprehensive regional databases, and integrating tephrochronology with spatially referenced environmental and archaeometric data into 3-D reconstructions using GIS and geostatistics.