The simple symmetric exclusion process (SSEP) has many nice properties, and sometimes is considered as a solvable model. The non-gradient exclusion process, also called speed-change exclusion process, is thus proposed to understand the more universal behavior. This talk summarizes some recent progresses on this model, especially with a focus on the combination of the quantitative homogenization and the classical techniques. The talk is based on my joint work with Tadahisa Funaki, Arianna Giunti, Jean-Christophe Mourrat, Maximilian Nitzschner, Han Wang, and Linzhi Yang.
