  Image denoising (removal of additive white Gaussian noise from an image) is
one of the oldest and most studied problems in image processing. An extensive
work over several decades has led to thousands of papers on this subject, and
to many well-performing algorithms for this task. Indeed, 10 years ago, these
achievements have led some researchers to suspect that "Denoising is Dead", in
the sense that all that can be achieved in this domain has already been
obtained. However, this turned out to be far from the truth, with the
penetration of deep learning (DL) into image processing. The era of DL brought
a revolution to image denoising, both by taking the lead in today's ability for
noise removal in images, and by broadening the scope of denoising problems
being treated. Our paper starts by describing this evolution, highlighting in
particular the tension and synergy that exist between classical approaches and
modern DL-based alternatives in design of image denoisers.
  The recent transitions in the field of image denoising go far beyond the
ability to design better denoisers. In the 2nd part of this paper we focus on
recently discovered abilities and prospects of image denoisers. We expose the
possibility of using denoisers to serve other problems, such as regularizing
general inverse problems and serving as the prime engine in diffusion-based
image synthesis. We also unveil the idea that denoising and other inverse
problems might not have a unique solution as common algorithms would have us
believe. Instead, we describe constructive ways to produce randomized and
diverse high quality results for inverse problems, all fueled by the progress
that DL brought to image denoising.
  This survey paper aims to provide a broad view of the history of image
denoising and closely related topics. Our aim is to give a better context to
recent discoveries, and to the influence of DL in our domain.
