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Classical inverse rendering approaches aim to decompose a scene into its orthogonal constituting elements, namely scene geometry, illumination and surface materials, which can later be used for augmented reality or to render new images under novel lighting or viewpoints. Recently, the application of deep neural computing to illumination estimation, relighting and inverse rendering has shown promising results. This contribution aims to bring together in a coherent manner current advances in this conjunction. We examine in detail the attributes of the proposed approaches, presented in three categories: scene illumination estimation, relighting with reflectance\u2010aware scene\u2010specific representations and finally relighting as image\u2010to\u2010image transformations. Each category is concluded with a discussion on the main characteristics of the current methods and possible future trends. 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