Finite groups of Lie type provide an extremely rich source of
examples for group theory and representation theory because they form a bridge between the discrete and continuous worlds. Deligne and Lusztig classified their representation theory following Drinfeld's crucial inspiration from the Langlands program. We describe how Deligne-Lusztig theory can be augmented using recent advances in the Taylor-Wiles method to obtain classifications for modular and integral representations of the finite linear group GL(3,q). This is joint work with B. Le Hung, B. Levin, and S. Morra.