1. An array of vertically stacked tiers of nonvolatile memory cells, comprising: a plurality of horizontally oriented first electrode lines within individual tiers of memory cells; a plurality of horizontally oriented global second electrode lines having local vertical second electrode line extensions extending through multiple of the tiers of memory cells; and individual of the memory cells comprising: a crossing one of the horizontal first electrode lines and one of the local vertical second electrode line extensions; programmable material, a select device in series with the programmable material, and current conductive material in series between and with the programmable material and the select device; the programmable material and the select device being in series with such crossing ones of the horizontal first electrode lines and local vertical second electrode line extensions; and the programmable material and the select device are oriented for predominant current flow into or out of the crossing one local vertical second electrode line extension out of or into, respectively, one of the programmable material or select device in a horizontal direction, and for predominant current flow into or out of the crossing one horizontal electrode line out of or into, respectively, the other of the programmable material and select device in a vertical direction.