In the European Union (EU), a total of 11,301,345 hectares are dedicated to the cultivation of fruit trees, mainly olive orchards, grapevines, nut trees (almond, walnut, chestnut, hazelnut, and pistachio), apple and pear trees, stone fruit trees (peach, nectarine, apricot, cherry, and plum), and citrus fruit trees (orange, clementine, satsuma, mandarin, lemon, grapefruit, and pomelo). Pruning these trees, together with plantation removal to a lesser extent, produces a huge amount of wood waste. A theoretical calculation of the wood waste in the European Union estimates approximately 2 and 25 million tons from wood plantation removal and pruning, respectively, per year. This wood waste is usually destroyed by in-field burning or crushing into the soil, which result in no direct economic benefits. However, wood from tree pruning, which is enriched in high added-value molecules, offers a wide spectrum of possibilities for its valorization. This review focuses on the contribution of wood waste to both sustainability and the circular economy, considering its use not only as biomass but also as a potential source of bioactive compounds. The main bioactive compounds found in wood are polyphenols, terpenes, polysaccharides, organic compounds, fatty acids, and alkaloids. Polyphenols are the most ubiquitous compounds in wood. Large amounts of hydroxytyrosol (up to 25 g/kg dw), resveratrol (up to 66 g/kg dw), protocatechuic acid (up to 16.4 g/kg), and proanthocyanins (8.5 g/kg dw) have been found in the wood from olive trees, grapevines, almond trees and plum trees, respectively. The bioactivity of these compounds has been demonstrated at lower concentrations, mainly in vitro studies. Bioactive compounds present antioxidant, antimicrobial, antifungal, biostimulant, anti-inflammatory, cardioprotective, and anticarcinogenic properties, among others. Therefore, wood extracts might have several applications in agriculture, medicine, and the food, pharmaceutical, nutraceutical, and cosmetics industries. For example, olive tree wood extract reduced thrombin-induced platelet aggregation in vitro; grapevine tree wood extract acts a preservative in wine, replacing SO₂; chestnut tree wood extract has antifungal properties on postharvest pathogens in vitro; and stone tree wood extracts are used for aging both wines and brandies. Moreover, the use of wood waste contributes to the move towards both a more sustainable development and a circular economy.