Corylus avellana (hazelnut) is one of the most popular tree nuts on a worldwide basis. The main products of C. avellana are kernels, a nutritious food, with a high content of healthy lipids, contained in a hard shell. In recent years, along with the ongoing research carried out on hazelnut kernels, a growing interest has been addressed to the hazelnut byproducts including hazelnut skin, hazelnut hard shell, and hazelnut green leafy cover as well as hazelnut tree leaf. These byproducts deriving from the roasting, cracking, shelling/hulling, and harvesting processes have been found as a source of “phytochemicals” with biological activity. The aim of this review is to provide a comprehensive and critical update on the chemistry and biological activity of specialized metabolites occurring in hazelnut kernels and byproducts. Phenolics are the most abundant phytochemicals not only in the kernels, but also in other processing byproducts. Attention has been also devoted to taxane derivatives isolated from C. avellana leaves. An overview on the biological activity, mainly antioxidant, antiproliferative, and antimicrobial along with less common biological effects, has been provided, contributing to highlight C. avellana as a source of bioactive phytochemicals with the potential to exert beneficial effects on human health. Finally, analytical techniques for the quali-quantitative analysis of specialized metabolites occurring in the different parts of C. avellana have been reviewed.