We summarize four emerging concepts in salt tectonics in the deepwater Gulf of Mexico, selected from a longer list of concepts that have advanced significantly in the last decade. Squeezed salt stocks are common in orogenic forelands, in inverted basins and at the toe of salt-bearing passive margins. Modelling suggests that during early shortening, an inward salt plume from the source layer inflates the diapir and arches its roof. After further shortening, diapiric salt is expelled as an outward plume back into the source layer. Salt canopies are conventionally thought to advance by glacial extrusion. However, almost all modern salt canopies are now buried and can only advance by frontal thrusting. Thrusting allows the salt canopy and its protective roof to advance together, minimizing salt dissolution. Advance is by a roof-edge thrust rooted in the leading tip of salt or by thrust imbricates forming accretionary wedges. Minibasins can sink into salt if the average density of the overburden exceeds that of salt. This requires 2–3 km of burial of siliciclastic fill, yet most minibasins first sink when much thinner. Three alternative mechanisms to negative buoyancy in the deepwater Gulf of Mexico address this paradox of initiation. First, squeezed diapirs inflate, leaving the intervening minibasins as depressions. Second, when a diapir's salt supply wanes, the overlying dynamic salt bulge subsides, allowing a minibasin to form. Third, differential loading causes the thick end of a sedimentary wedge to sink faster into the salt, creating a sag. Spreading salt canopies can transport their dismembered roof fragments tens of kilometres basinward. These exotic fragments are up to 25 km in breadth and comprise anomalously old Mesozoic through Miocene sequences. Strata of the same age underlie the salt canopy or its welded equivalent, signalling lateral transport by thick salt.