In 2006, Labourie introduced Anosov representations to investigate a special connected component of the character variety of representations of Fuchsian groups into PSL(d,R) discovered by Hitchin, shown to consist entirely of discrete and faithful representations. Guichard-Wienhard generalized Labourie's definition to word-hyperbolic groups, and Anosov representations have since grown to become a widely accepted generalization of convex cocompact Fuchsian groups to higher rank, exhibiting interesting and desirable dynamical and geometric properties at infinity along with a deformation theory that has many similarities and differences with classical Teichmuller theory. In this talk, we will introduce Anosov representations and survey recent results towards understanding the hyperbolic groups which admit Borel Anosov representations into SL(d,R), which are the "most Anosov" kinds of Anosov representations. This is a candidacy talk.