Descent methods of optimisation depend on calculating the derivatives of the composite function with respect to the large number of model parameters. Adjoint techniques allow the computation of derivatives in such complex models, with much less calculation than direct methods, and so enable practical non-linear inversion.Adjoint methods also allow effective computation of sensitivity kernels associated with the variation of critical parameters for both structure and sources. Sensitivity kernels can provide insight into the nature of Earth structure and the potential resolution of seismic tomography.