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In this review, we present the applications of the wavelet transform in de-noising, compression, pattern classification and prediction of signals. Opening section of the article deals with technical overview of the wavelets. Application review wraps the major application domain of continuous, discrete and wavelet packet transforms in conventional and non conventional fields of engineering. In application review, we provide brief background information about the type of wavelet transform used with its implications on the results. Final section presents the denoising and compress results of the olfactory signal using the most commonly applied wavelet transform i.e. Daubechies D4, D8 and D20 wavelets with the 3rd and 6th level of decomposition. The compression results reveled that the level of decomposition affected more on the compression results than the order of the mother wavelet. Furthermore, as the level of decomposition increased the compressed signal had undersized distortion during the reconstruction of a signal.