Wavelets have become a popular tool in many research areas because of the combination of a nice theoretical foundation and promising applications. The theoretical foundation reveals new insights and has thrown a new light on several application areas. One of the applications is speckle reduction and enhancement of synthetic aperture radar (SAR) images. The use of wavelet thresholding as noise reduction method is based on the following properties: Wavelet transformation creates a sparse signal (because of the decorrelation property of the transform); noise is spread out equally over all wavelet transform coefficients; noise level is not too high and thus signal wavelet transformation coefficients can be recognized. In this paper, we will review the use of wavelet,translation invariant wavelet, almost translation invariant wavelet (complex wavelet), and multi-wavelet transformations in speckle reduction of SAR images. Several nonlinear thresholding functions, i.e., hard, soft, adaptive sigmoid, and a function based on generalized cross validation are investigated and compared in experiments.