Coal, one of the most complex geological materials, consists of organic and mineral matter, the latter including crystalline minerals, non-crystalline mineraloids, and elements with non-mineral associations. Overall, the modes of occurrence of elements in coal are classified into organic, mineral, and intimate organic associations, the latter including those adsorbed on to the surface of organics, dissolved in pore waters, and hosted in very fine-grained minerals (sub-micro- or nano-minerals) encased in or shielded by the organic matter of coal. Mineral associations, defined as elements associated with minerals are straightforward; however, confusion about organic and intimate organic associations of elements usually arise in the literature. Understanding organic, mineral, and intimate organic associations of elements is important not only because non-mineral elements and, to a lesser extent, elements associated with fine-grained minerals, play a significant role in affecting the utilization of coal, but also such modes of occurrence of elements provide useful geochemical information on coal formation and coal-bearing basin evolution. With a few exceptions (such as Cd, Nb, Ta, Zr, and Hf), most elements determined in coal, particularly in low-rank coal, have varying-degrees of organic association. In this paper, we review the definition of associations of non-mineral elements in coal, as well as their methods of determination, and then review the associations of selected elements including environmentally-sensitive (e.g., S, As, U, and Hg) and critical elements, the latter of which drive some of the significant advancements in technology and energy efficiency in the world today (e.g., rare earth elements and Y, Ge, and U), and some major elements (e.g., Ca, Mg, Fe, Al, and Ti) that largely occur in non-mineral forms in low-rank coals. •The modes of occurrence of elements in coal are classified into organic, mineral, and intimate organic associations•The intimate organic associations include those adsorbed on to the surface of organics, dissolved in pore waters, and hosted in very fine-grained minerals.•Most elements determined in coal have varying-degrees of organic association.