In a number of technologies computational and experimental mechanics join for the solution of inverse problems. Concrete dams are referred to in this lecture, which is intended to outline and briefly discuss recent research results on representative inverse problems in structural engineering, namely: diagnostic overall analysis of a dam monitored by radar, under hydrostatic loading, in the possible presence of damages due to alkali-silica reaction; identification of local stresses, stiffness and strength by means of a two-holes dilatometric technique; stochastic calibration of a piecewise-linear cohesive crack model for concrete by wedge splitting tests and extended Kalman-Bucy filter