Due to relativistic bulk motion, the structure and orientation of gamma-ray burst (GRB) jets have a fundamental role in determining how they appear. The recent discovery of the GW170817 binary neutron star merger and the associated GRB boosted the interest in the modeling and search for signatures of the presence of a (possibly quasi-universal) jet structure in long and short GRBs. In this review, following a pedagogical approach, we summarize the history of GRB jet structure research over the last two decades, from the inception of the idea of a universal jet structure to the current understanding of the complex processes that shape the structure, which involves the central engine that powers the jet and the interaction of the latter with the progenitor vestige. We put some emphasis on the observable imprints of jet structure on prompt and afterglow emission and on the luminosity function, favoring intuitive reasoning over technical explanations.