We discuss mantle structure and dynamics under the Gibraltar arc. For that region, a large variety of geodynamic models has been proposed, and there was, up to recently, no consensus on which of these models is the best one to describe the geodynamic situation of the region. The key to distinguishing the different models probably lies in the upper mantle, and we propose two specially adapted seismological techniques that help to distinguish each of the two models that are more frequently invoked. These are, on one hand, the subduction-rollback (SR) model, and on the other, continental delamination or convective removal (CDCR). The first technique that we use is based on observations of dispersed P-wavetrains that are expected for certain ray directions. Observations made on the Gibraltar arc suggest the presence of subducted oceanic lithosphere under the Alboran Sea. The second technique is based on shear-wave splitting of SKS phases, and it allows us to look for the radially-oriented flow that must be present in the mantle beneath the Alboran Sea, for a CDCR mechanism. There are however no indications of any radial flow up to this point. Both approaches therefore suggest that subduction-rollback is the best model to explain the complex geodynamic situation under the region.