I'm going to discuss a recurring theme in my research: the interactions between algebraic combinatorics and modular representation theory. This means trying to find combinatorial descriptions of objects in modular representation theory, and trying to use tools from modular representation theory to solve problems in algebraic combinatorics. I'll focus on a couple of recent examples: a combinatorial description of an analog of the ring of symmetric functions for representations of GL_n(F_q) in defining characteristic, and a proof of a tensor-cube version of the Saxl conjecture in combinatorial representation theory using representations in characteristic 2.