Some embodiments include memory cells. The memory cells may have a first electrode, and a trench-shaped programmable material structure over the first electrode. The trench-shape defines an opening. The programmable material may be configured to reversibly retain a conductive bridge. The memory cell may have an ion source material directly against the programmable material, and may have a second electrode within the opening defined by the trench-shaped programmable material. Some embodiments include arrays of memory cells. The arrays may have first electrically conductive lines, and trench-shaped programmable material structures over the first lines. The trench-shaped structures may define openings within them. Ion source material may be directly against the programmable material, and second electrically conductive lines may be over the ion source material and within the openings defined by the trench-shaped structures.