Cluster-assembled materials combine the nanoscale size and composition-dependent properties of clusters, which have highly tunable magnetic and electronic properties useful for a great variety of potential technologies. To understand the emergent properties as clusters are assembled into hierarchical materials, we have synthesized 23 cluster-assembled materials composed of As7(3-)-based motifs and different countercations and measured their band gap energies. We found that the band gap energy varies from 1.09 to 2.21 eV. In addition, we have carried out first principles electronic structure studies to identify the physical mechanisms that enable control of the band gap edges of the cluster assemblies. The choice of counterion has a profound effect on the band gap energy in ionic cluster assemblies. The top of the valence band is localized on the arsenic cluster, while the conduction band edge is located on the alkali metal counterions. Changing the counterion changes the position of the conduction band edge, enabling control of the band gap energy. We can also vary the architecture of the ionic solid by incorporating cryptates as counterions, which provide charge but are separated from the clusters by bulky ligands. Higher dimensionality typically decreases the band gap energy through band broadening; however band gap energies increased upon moving from zero-dimensional (0D) to two-dimensional (2D) assemblies. This is because internal electric fields generated by the counterion preferentially stabilize the adjacent lone pair orbitals that mark the top of the valence band. Thus, the choice of the counterion can control the position of the conduction band edge of ionic cluster assemblies. In addition, the dimensionality of the solid via internal electric fields can control the valence band edge. Through covalently linking arsenic clusters into composite building blocks, we have also been able to tune the band gap energy. We used a theoretical description based on cluster orbital theory to provide microscopic understanding of the electronic character of the composite building blocks and the observed variations in the band gap energy. Also, we have shown how dimeric linkers can be used to control the band gap energy. Lastly, we also investigated the effects of charge transfer complexes of M(CO)3 on the band gap energy.