Sugar-derived humins and melanoidins figure significantly in food chemistry, agricultural chemistry, biochemistry, and prebiotic chemistry. Despite wide interest and significant experimental attention, the amorphous and insoluble nature of the polymers has made them resistant to conventional structural characterization. Here we make use of solid-state NMR methods, including selective (13)C substitution, (1)H-dephasing, and double quantum filtration. The spectra, and their interpretation, are simplified by relying exclusively on hydronium for catalysis. The results for polymers derived from ribose, deoxyribose, and fructose indicate diverse pathways to furans, suggest a simple route to pyrroles in the presence of amines, and reveal a heterogeneous network-type polymer in which sugar molecules cross-link the heterocycles.