Nuts consumption has increased significantly in the last 10 years, especially driven by the stimulated awareness of their possible beneficial health effects. Increased nuts consumption is linked to an obvious accumulation of by-products and waste. With the view of the circular economy, the aim of this review is to analyse the recent and innovative approaches able to valorise the by-products derived from almonds and hazelnuts, two important nut products of the Italian scene, with historical and traditional importance. The most important solutions are concerned with reuse of almond hull, shell, skin, oil cake, and hazelnut shell; skin and oil cake are often considered waste or by-products. Many interesting implications in the feed and food sectors have been detected in the last ten years, aimed at designing innovative materials developed from by-products and extraction of bioactive molecules for different purposes. The perspective chosen to discuss the topic is related to the sustainability of these processes, in terms of both the environment and economy. The circular economy supports a zero-waste approach, which should not also be meant as a zero-cost process in terms of the level of technology that has been partially developed.