Different methods for the measurement of in-plane and out-of-plane nanodisplacements of microscopic samples are discussed and compared. It is shown that correlation methods are suited for in-plane displacement measurements and can achieve accuracies of a few nanometers. The method based on vortices tracking can be used for in-plane displacement measurements, but its accuracy is lower compared with the intensity correlation method. The holographic methods allow the measurement of in-plane and out-of-plane displacements at the same time; but in this case, a quite complex setup is required. A combination of correlation methods for in-plane measurement and digital holography for out-of-plane plane measurements is also discussed. The accuracy of the different methods was determined by comparison with a calibrated reference.