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.