The human heme enzymes tryptophan 2,3-dioxygenase (hTDO) and indoleamine 2,3 dioxygenase (hIDO) catalyze the initial step in L-tryptophan (L-Trp) catabolism, the insertion of dioxygen into L-Trp. Overexpression of these enzymes causes depletion of L-Trp and accumulation of metabolic products, and thereby contributes to tumor immune tolerance and immune dysregulation in a variety of disease pathologies. Understanding the assembly of the catalytically active, ternary enzyme-substrate-ligand complexes is not yet fully resolved, but an essential prerequisite for designing efficient and selective de novo inhibitors. Evidence is mounting that the ternary complex forms by sequential binding of ligand and substrate in a specific order. In hTDO, the apolar L-Trp binds first, decreasing active-site solvation and, as a result, reducing non-productive oxidation of the heme iron by the dioxygen ligand, which may leave the substrate bound to a ferric heme iron. In hIDO, by contrast, dioxygen must first coordinate to the heme iron because a bound substrate would occlude ligand access to the heme iron, so the ternary complex can no longer form. Consequently, faster association of L-Trp at high concentrations results in substrate inhibition. ... mehrHere, we summarize our present knowledge of ternary complex formation in hTDO and hIDO and relate these findings to structural peculiarities of their active sites.