This paper overviews basic principles and applications of the robust DFT (RDFT) approach, which is used for robust processing of frequency-modulated (FM) signals embedded in non-Gaussian heavy-tailed noise. In particular, we concentrate on the spectral analysis and filtering of signals corrupted by impulsive distortions using adaptive and nonadaptive robust estimators. Several adaptive estimators of location parameter are considered, and it is shown that their application is preferable with respect to non-adaptive counterparts. This fact is demonstrated by efficiency comparison of adaptive and nonadaptive RDFT methods for different noise environments.