We will discuss the realization of 2d $(0,2)$ gauge theories in terms of branes, focusing on Brane Brick Models, which are T-dual to D1-branes probing toric Calabi-Yau 4-folds. These brane setups fully encode the infinite class of 2d $(0,2)$ quiver gauge theories on the worldvolume of the D1-branes and substantially streamline their connection to the probed geometries. They also provide a brane realization of triality. In the second part of the talk, we will present a class of 4-dimensional crystal melting models that describe the BPS spectrum of D-branes on toric Calabi-Yau 4-folds. Their crystalline structures are determined by the corresponding brane brick models. The crystals provide a discretized version of the underlying toric geometries.