Sequence stratigraphy solved the basic problem that genetically related, but different, lithofacies were routinely assigned to different lithostratigraphic units defined by arbitrary vertical and horizontal cutoffs. Stratigraphically important stratal relationships, and especially stratal terminations (for example, lapout) can be observed in seismic data and can be documented in continuous outcrops, such as in the deserts of the Western Interior of North America and in closely spaced well-log data sets. In sparse data sets, interpolation of lapout patterns introduces uncertainty in correlation and designation of sequences and systems tracts and their associated surfaces. Diachroneity of fluvial terrace deposits is documented using detailed facies architectural studies, and calls into question the assumed chronostratigraphic significance of many so-called sequence boundaries identified in the rocks of the Cretaceous Interior Seaway of North America. Sequence boundaries, formed during prolonged sea-level falls, may be less chronostratigraphically significant than transgressive surfaces formed during rapid rises. As a consequence, flooding surfaces are theoretically more significant, and also have greater utility as allostratigraphic boundaries, although they may also exhibit diachroneity. Tectonic unconformities produce differential lithospheric deformation, which results in angular unconformities, although the angle of discordance may be very small. In the Cretaceous Interior Seaway of North America, such unconformities may be expressed by marine erosion in distal basin settings. Regional isochronous bentonites provide useful marker beds that clearly illustrate angular discordance. In the fluvial realm, such tectonic discontinuities may be indicated by changes in palaeocurrent orientations, as well as by provenance changes. Although sequence stratigraphy provides a powerful methodology and theoretical framework for correlating and understanding the evolution of stratigraphic successions in the context of changing accommodation, allostratigraphy remains the only accepted scheme for the formal naming of stratigraphic units based on bounding discontinuities. Whatever type of sequence stratigraphy or allostratigraphy is preferred, in all cases it is key to recognize that sequence stratigraphy, at its heart, is the re-ordering, correlation, and sometimes renaming of stratigraphic units on the basis of bounding discontinuities and their correlative surfaces, as opposed to the arbitrary lithofacies-oriented approach using broad facies zones (for example, ‘shazam lines’) or arbitrary cutoffs, such as is used in traditional lithostratigraphy.