Tame filling functions for finitely presented groups are a quasi-isometry invariant refinement of the intrinsic diameter (isodiametric) function and the extrinsic diameter function. In contrast to diameter functions, it is unknown if every pair of a finitely presented group G with presentation P, (G,P), has a finite-valued tame filling function. Within this talk, I will discuss major results involving tame filling functions and intrinsic tame filling functions for graph products (a generalization of direct and free products.