Hazelnuts are one of the most widely consumed nuts, but their production creates large quantities of by-products, especially shells, that could be upcycled into much more valuable products. Recent studies have shown that hazelnut shell hemicellulose is particularly rich in compounds that are potential precursors of xylooligosaccharides and arabino-xylooligosaccharides ((A)XOS), previously defined as emerging prebiotics very beneficial for human health. The production of these compounds on an industrial scale-up could have big consequences on the functional foods market. However, to produce (A)XOS from a lignocellulosic biomass, such as hazelnut shell, is not easy. Many methods for the extraction and the purification of these prebiotics have been developed, but they all have different efficiencies and consequences, including on the chemical structure of the obtained (A)XOS. The latter, in turn, is strongly correlated to the nutritional effects they have on health, which is why the optimization of the structural characterization process is also necessary. Therefore, this review aims to summarize the progress made by research in this field, so as to contribute to the exploitation of hazelnut waste streams through a circular economy approach, increasing the value of this biomass through the production of new functional ingredients.