The paper presents recent theoretical developments and numerical results obtained at NASA Langley Research Center, by Dr. Alex Tessler and co-workers, and at Politecnico di Torino, by the AESDO Group, addressing the inverse problem of "shape-sensing", i.e., reconstruction of structural displacements using surface-measured strains. The theoretical framework of the inverse Finite Element Method (iFEM) is briefly presented. Both the original formulation for built-up shell structures and the recent formulation for truss, beam, and frame structures are described. Several numerical and experimental results for plate- and beam-like structures subjected to static and dynamic loads are presented. It is shown that iFEM is a valid approach for shape sensing due to its computational efficiency, accuracy, and robustness with respect to experimental strain-measurement errors. The iFEM shape-sensing methodology is particularly attractive because it does not require any information regarding applied loading, elastic material constants, inertial properties, or damping characteristics