Any hypothesis for the origin of the Martian global dichotomy should survive three elementary tests: (1) it must account for the observed plan shape and apparent depth of the Martian northern lowland, (2) it must be physically consistent, and (3) it must be compatible with available geological and geophysical data. At present, there are three contending types of hypotheses for the origin of the dichotomy: creation by some endogenic process or processes, creation by a single mega-impact, or creation by several overlapping large impacts. None of these hypotheses can survive all three tests without the incorporation of additional processes. The endogenic and mega-impact hypotheses require the presence of additional impact basins to explain many of the topographic details of the Martian northern lowland and of the dichotomy boundary, and the mega-impact hypothesis probably also requires extensive primordial erosion. The multiple-impact hypothesis requires an additional process or processes to account for the large portion of the northern lowland that is external to the rims of the basins inferred to be the cause of the lowland. While we believe that aspects of the multiple-impact hypothesis are required to account for some topographic details of the boundary and of the lowland, other processes appear better able to account for the dichotomy as a whole. These could include an early mega-impact, endogenic processes, or some combination of these.