Damage to structural walls in the recent earthquakes in Chile (2010) and New Zealand (2011) demonstrated that modern reinforced concrete (RC) walls may not achieve the expected ductile response but could possibly be triggered by out-of-plane displacements of the wall. Following a review of the mechanisms that cause global out-of-plane buckling of RC walls, relevant international code requirements, and past experimental tests, this paper describes the findings from quasi-static cyclic tests of two thin RC walls with single layers of vertical and horizontal reinforcement. The two walls were subjected to uni-directional (in-plane) and bi-directional (in-plane and out-of-plane) loading respectively. Both walls experienced significant out-of-plane displacements and damage caused by out-of-plane deformations ultimately triggered the wall in-plane failure. The data obtained with extensive instrumentation of the test units, which included optical measurements of the 3D displacement field, yield new insights into the development of out-of-plane displacements, in particular with regard to: evolution of out-of-plane displacements with imposed in-plane displacements, portion of height and length of the wall that are involved in the out-of-plane instability, influence of both local and global tensile strains on the buckling behaviour and role of bi-directional loading on out-of-plane instability. The tests showed that very significant out-of-plane displacements—larger than half of the wall thickness—can take place without causing out-of-plane wall failure. The damage caused by these large out-of-plane displacements, however, can lead to a premature in-plane failure of the wall.