The available experimental data on non-linear microwave effects in sup
erconductors and some theoretical explanations of these, published sin
ce 1964, are reviewed. Various mechanisms of non-linearity observed un
der a wide variety of external conditions and in a broad spectrum of m
aterials are discussed. Some examples of application of the non-linear
ity to frequency mixing are considered and analysed in the framework o
f a simple model of a fast-response resistive mixer.