This dissertation describes methods of mitigating radio frequency interference (RFI) in the frequency range 10-100 MHz, developing and evaluating coherent methods with which RFI is subtracted from the afflicted data, nominally resulting in no distortion of the underlying signals. This approach is of interest in weak signal applications such as radio astronomy, where the signal of interest may have interference-to-noise ratio much less than one, and so can be easily distorted by other methods. Environmental noise in this band is strong and non-white, so a realistic noise model is developed, with which we characterize the performance of signal parameter estimation, a key component of the proposed algorithms. Two classes of methods are considered: "generic" parameter estimation/subtraction (PE/S) and a modulation-specific form known as demodulation-remodulation ("demod--remod") PE/S. It is demonstrated for RFI in the form of narrowband FM and Broadcast FM that generic PE/S has the problem of severely distorting underlying signals of interest and demod-remod PE/S is less prone to this problem. Demod-remod PE/S is also applied and evaluated for RFI in the form of Digital TV signals. In both cases, we compare the performance of the demod-remod PE/S with that of a traditional adaptive canceling method employing a reference antenna, and propose a hybrid method to further improve performance. A new metric for "toxicity" is defined and employed to determine the degree to which RFI mitigation damages the underlying signal of interest.