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Frequency-domain nonlinear analysis techniques for the simulation of active microwave circuits solve the linear and nonlinear network equations entirely in the frequency-domain. By so doing, they avoid the aliasing problems inherent in piecewise harmonic balance approaches. Consequently, frequency-domain techniques have extremely wide dynamic range and easily accommodate high order multitone excitation. However, this is at the expense of requiring more restrictive nonlinear device models. There are a large number of frequency-domain nonlinear analysis techniques but all are based on functional expansions which enable the frequency components of the output spectrum to be calculated directly from the input spectrum. These techniques have been used to analyze many nonlinear circuits and are the only candidates for the hierarchical simulation of nonlinear microwave circuits. This paper first uses frequency-domain concepts to discuss nonlinear distortion phenomena, then, a review of the frequency-domain nonlinear analysis literature is made with the aim of presenting the major advances in these techniques.