Allochthonous salt sheets advance in four ways: (1) extrusive advance, (2) open-toed advance, (3) thrust advance, and (4) salt-wing intrusion. These mechanisms are determined primarily by the geometry and thickness of the roof that overlies the advancing sheet. An extrusive sheet spreads without a roof or with a roof of negligible mechanical strength. An open-toed sheet is partially covered by a mechanically significant roof but has an extrusive toe. An overthrusting sheet advances along a thrust fault at its leading edge, carrying its roof with it. A salt wing intrudes from the flank of a diapir into a shallower salt layer. Extrusive, open-toed, and over-thrusting salt sheets are found in both passive margins and orogens. A sheet typically evolves through two or more of these mechanisms. Three lineages, or evolutionary paths, are common. Plug-fed extrusions emanate from the top of a salt dome or salt wall. Plug-fed thrusts form the base of the hanging wall of thrust faults that are rooted in the tops of salt domes or salt walls. Finally, source-fed thrusts initiate as thrust faults rooted in the autochthonous salt layer. Source-fed thrusts form the largest individual salt sheets, some covering thousands of square kilometers. Salt-wing intrusions form only under special circumstances, so they are not part of the three major lineages. These intrusions are restricted to compressionally inverted basins containing multiple salt layers and are known only in the Zechstein salt basin.