This article presents a review of our present understanding of the spin structure of the unpolarized hadron. Particular attention is paid to the quark sector at leading twist, namely, the quark Boer–Mulders function, which describes the transverse polarization of the quark inside an unpolarized hadron. After introducing the operator definition of the Boer–Mulders function, a detailed treatment of different non-perturbative calculations of the Boer–Mulders functions is provided. The phenomenology in Drell–Yan processes and semi-inclusive leptoproduction, including the extraction of the quark and antiquark Boer–Mulders functions from experimental data, is presented comprehensively. Finally, prospects for future theoretical studies and experimental measurements are presented in brief.