Citrate, α-ketoglutarate and succinate are TCA cycle intermediates that also play essential roles in metabolic signaling and cellular regulation. These di- and tricarboxylates are imported into the cell by the divalent anion sodium symporter (DASS) family of plasma membrane transporters, which contains both cotransporters and exchangers. While DASS proteins transport substrates via an elevator mechanism, to date structures are only available for a single DASS cotransporter protein in a substrate-bound, inward-facing state. We report multiple cryo-EM and X-ray structures in four different states, including three hitherto unseen states, along with molecular dynamics simulations, of both a cotransporter and an exchanger. Comparison of these outward- and inward-facing structures reveal how the transport domain translates and rotates within the framework of the scaffold domain through the transport cycle. Additionally, we propose that DASS transporters ensure substrate coupling by a charge-compensation mechanism, and by structural changes upon substrate release.