I will present several new results in the intersection of cluster algebras and polylogarithm functions motivated by the study of scattering amplitudes. For example, I will show how the iterated integral structure of polylogarithms can be intimately tied to the structure of cluster algebras through a property called cluster adjacency. As an example I will give a polylogarithm function of weight 4 related to the A_2 cluster algebra. I will then discuss systematic ways in which larger cluster algebras can be associated with more complicated polylogarithm functions, such as scattering amplitudes, through various subalgebra decompositions.