An array of memory cells, comprising: a first electrically conductive line extending along a first direction; a plurality of trench-shaped programmable material structures over the first electrically conductive line; the trench-shaped programmable material structures extending along a second direction which intersects the first direction; the individual trench-shaped programmable material structures having openings that extend into the programmable material, the structures having sidewalls comprising the programmable material, the trench-shaped programmable material structures being configured to reversibly retain conductive bridges within individual memory cells to transition the memory cells between low and high resistive states; ion source material comprised by the individual memory cells and being directly against the trench-shaped programmable material structures, the ion source material only partially filling the opening to leave a remaining portion of the opening over the ion source material; second electrically conductive lines that extend into the openings over the ion source material and are defined by the trench-shaped programmable material structures; individual memory cells comprising regions of programmable material and ion source material directly between the first and second electrically conductive lines; and wherein the first and second electrically conductive lines, and the programmable material and ion source material between the first and second electrically conductive lines, together form a first level of the array; the first level having a vertical arrangement from the first electrically conductive line to the second electrically conductive lines; and further comprising a second level over the first level; said second level having either the same vertical arrangement as the first level or having an opposite vertical arrangement relative to the first level. a first electrically conductive line extending along a first direction; a plurality of trench-shaped programmable material structures over the first electrically conductive line; the trench-shaped programmable material structures extending along a second direction which intersects the first direction; the individual trench-shaped programmable material structures having openings that extend into the programmable material, the structures having sidewalls comprising the programmable material, the trench-shaped programmable material structures being configured to reversibly retain conductive bridges within individual memory cells to transition the memory cells between low and high resistive states; ion source material comprised by the individual memory cells and being directly against the trench-shaped programmable material structures, the ion source material only partially filling the opening to leave a remaining portion of the opening over the ion source material; second electrically conductive lines that extend into the openings over the ion source material and are defined by the trench-shaped programmable material structures; individual memory cells comprising regions of programmable material and ion source material directly between the first and second electrically conductive lines; and wherein the first and second electrically conductive lines, and the programmable material and ion source material between the first and second electrically conductive lines, together form a first level of the array; the first level having a vertical arrangement from the first electrically conductive line to the second electrically conductive lines; and further comprising a second level over the first level; said second level having either the same vertical arrangement as the first level or having an opposite vertical arrangement relative to the first level.