Fionn Murtagh Dept. Computer Science, Royal Holloway, University of London, Egham, UK e-mail: fmurtagh@acm.orgThis chapter reviews different astronomical deconvolution methods. The all-pervasive presence of noise is what makes deconvolution particularly difficult. The diversity of resulting algorithms reflects different ways of estimating the true signal under various idealizations of its properties. Different ways of approaching signal recovery are based on different instrumental noise models, whether the astronomical objects are point-like or extended, and indeed on the computational resources available to the analyst. We present a number of recent results in this survey of signal restoration, including in the areas ofsuper-resolution and dithering. In particular we show that most recent published work has consisted of incorporating some form of multiresolution in the deconvolution process. Finally we show how the deconvolution techniques can be extended to the case of blind deconvolution.