A combination of neutron diffraction (ND), 6Li magic-angle spinning NMR, electrochemistry, and first principles calculations have been used to determine and rationalize the structural changes that occur during cycling of the layered material Lix(Ni0.5Mn0.5)O2 (x = 1), synthesized via the hydroxide route. ND and 6Li NMR experiments confirm that Li is lost from the transition metal (TM) layers, very early on in the charge process. On charging to higher voltages (above 4.5 V), the Li is lost from the tetrahedral and residual Li octahedral sites in the Li layers. This process is accompanied by a migration of more than 75% of the Ni ions originally present in the Li layers into the TM layers, to occupy the sites vacated by Li. Calculations suggest that (i) these Ni migrations occur via the tetrahedral sites, (ii) activation energies for migration depend strongly on the original position of the Ni ions in the Li layers though the driving force for migration is large (>1 eV), and (iii) because neither Ni3+ nor N...