The ability to extract the history of motions associated with geologic structures is a key element in understanding fundamental deformation processes, for example, the growth of folds or faults in three dimensions, the interactions between faults, and the spatial relationships between deformation and sedimentation. Here, we show how to extract these motions for complexly faulted and folded structures using a new method of three-dimensional (3-D) restoration. We perform the restoration on sets of stratigraphic horizons defined in three dimensions as irregular triangular networks (triangulated surfaces), with the unfaulting and unfolding as separate steps. The unfolding is achieved by a best-fit packing of the triangular surface elements, implementing several restoration mechanisms, including (1) flexural slip, (2) homogeneous inclined shear, and (3) 3-D inclined shear oriented in the azimuth of the local surface dip. After unfolding, we restore the displacement on the faults in map view by a best-fit rigid-body packing of fault blocks in a way that allows for complex systems of faults. By performing the combined unfolding and unfaulting with multiple orientations of the unfolding vectors, we determine the optimum combination of unfolding plus unfaulting, which yields a best estimate of the surface-strain fields, the particle-displacement field, and the fault-slip vectors in three dimensions. We illustrate the restoration method with synthetic examples and a complexly faulted structure from the western Niger Delta that is imaged in 3-D seismic data. We include the results of tests to quantify some potential sources of error in the restorations.