  We present a detailed review of large-scale structure (LSS) study using the
discrete wavelet transform (DWT). After describing how one constructs a wavelet
decomposition we show how this bases can be used as a complete statistical
discription of LSS. Among the topics studied are the the DWT estimation of the
probability distribution function; the reconstruction of the power spectrum;
the regularization of complex geometry in observational samples; cluster
identification; extraction and identification of coherent structures;
scale-decomposition of non-Gaussianity, such as spectra of skewnes and kurtosis
and scale-scale correlations. These methods are applied to both observational
and simulated samples of the QSO Lyman-alpha forests. It is clearly
demonstrated that the statistical measures developed using the DWT are needed
to distinguish between competing models of structure formation. The DWT also
reveals physical features in these distributions not detected before. We
conclude with a look towards the future of the use of the DWT in LSS.
