Frames are collections of vectors in Hilbert spaces which have reconstruction properties akin to orthonormal bases. In order for such a representation system to be robust in applications, one often asks that the vectors be geometrically spread apart; that is, the pairwise angles between the lines they span should be as large as possible. It ends up that structures in combinatorial design theory, like difference sets and balanced incomplete block designs (BIBDs), can be used in different ways to construct optimal configurations. Furthermore, the linear dependencies of the vectors are often encoded as BIBDs. The orbit of a vector under a group action sometimes also yields optimal configurations. There are infinite classes of optimal frames, like the so-called Gabor-Steiner ETFs, which have both group symmetry and a combinatorial construction. In this talk, these and other connections between frames and algebraic combinatorics, combinatorial design theory, algebraic graph theory, and more will be presented. Some open conjectures in frame theory and quantum information theory will also be discussed.