A three-dimensional array of memory elements is formed across multiple layers of planes positioned at different distances above a semiconductor substrate. The memory elements reversibly change a level of electrical conductance in response to a voltage difference being applied across them. The three-dimensional array includes a two-dimensional array of pillar lines from the substrate through the multiple layers of planes. A first set of pillar lines acts as local bit lines for accessing the memory elements together with an array of word lines on each plane. A second set of pillar lines is connected to the word lines. An array of metal lines on the substrate is switchable connected to the pillar lines to provide access to the first and second sets of pillar lines, thereby to provide access respectively to the bit lines and word lines of the three-dimensional array.