In this Chapter, we review the basic principles of image restoration, and we discuss in more detail a new state-of-the art approach with applications in biomedical image processing. While the term image restoration is widely used in connection with the removal of various types of degradations, we address image restoration in the classical sense, which means estimating the underlying degradation-free image from the observations affected by noise and blur. This estimation process makes use of the degradation model of the image formation (for noise and blurring), which is often referred to as the data distribution. Next to this degradation model, the restoration process often makes use of a prior model, which encodes our prior knowledge about the image to be estimated, e.g., some of its statistical properties. The use of these models and clearly defined criteria for optimally estimating true values of the underlying degradation-free data, is what makes image restoration essentially different from image enhancement techniques (which are mainly heuristic and aim at improving the visual perception of the image only). In this Chapter, we address the Bayesian restoration framework, and we discuss the use of some popular statistical models, like multiresolution image representations. There we will illustrate the advantages of using geometry-adaptive representations with improved orientation selectivity (like complex wavelets, curvelets, shearlets and steerable pyramids) over the classical wavelets. Finally, we will present several applications in restoration of biomedical images obtained with a confocal microscope (an special kind of optical microscope that allows 3D imaging).