Duality for toric Landau-Ginzburg models unifies the many mirror constructions found in the literature for complete intersections in toric varieties. Furthermore, their toric structure suggests that homological mirror symmetry for dual pairs can be attacked directly using T-duality. I will discuss this approach, and a generalization of T-duality that has arisen while attempting to implement it. Time permitting, I will also talk about a recent project with Josh Guffin in which we give a mirror construction for (0,2) toric Landau-Ginzburg models near the (2,2) locus.