The objectives of this narrative review are as follows: an evaluation of the bromatological composition of hazelnuts and a comparison of the nutritional properties of raw versus roasted hazelnuts, taking into account potential differences among varieties from different production territories such as Turkey, Italy, Chile, and New Zealand; an evaluation of nutrients contained in hazelnut skin; and an evaluation of nutrients contained in hazelnut oil. This review incorporates 27 scientific articles that measured and reported the concentrations of macro- and micro-nutrients in hazelnuts. These hazelnuts were subjected to different processing methods, originated from various geographical areas, or belonged to different varieties. Our results showed that the different varieties and territories where the hazelnuts were cultivated influence their bromatological composition, and we found that different processing steps can largely influence the concentration of specific nutrients. The removal of the skin, which contains a very high concentration of compounds with antioxidant action, is particularly critical. We should give greater attention to the skin, considering it not as a waste product, but as an important part of the hazelnut due to its nutritional properties of primary relevance in the Mediterranean diet. We provide a detailed assessment of the nutritional properties of the hazelnut kernel, skin, and oil, evaluating nutrient compositions and possible modifications (increases or reductions) that occur during the roasting process or that depend on the production territory and origin.