The wavelet transform and multiresolution analysis are presented. They are used in two applications: fusion of images having different spatial and spectral resolutions, and speckle removal in radar imagery. A method was developed in data fusion for synthesizing images having the best of the available spatial resolutions yet preserving the quality of the spectral information. An existing filter for speckle removal was improved with the combination of these two tools. Other filters may be similarly improved thus obtaining a decrease of the speckle effects in homogeneous areas yet preserving geometrical information. It is concluded on the benefits of the wavelet transform and multiresolution analysis in remote sensing and perspectives are discussed.