Robust magnetotelluric (MT) response function estimators are now in standard use by the induction community. Properly devised and applied, these have ability to reduce the influence of unusual data (outliers). The estimators always yield impedance estimates which are better than the conventional least square (LS) estimation because the ‘real’ MT data almost never satisfy the statistical assumptions of Gaussian distribution and stationary upon which normal spectral analysis is based. This paper discuses the development and application of robust estimation procedures which can be classified as M‐estimators to MT data. Starting with the description of the estimators, special attention is addressed to the recent development of a bounded‐influence robust estimation, including utilization of the Hilbert Transform (HT) operation on causal MT impedance functions. The resulting robust performances are illustrated using synthetic as well as real MT data.