Anion transport across phospholipid membrane is a typical supramolecular function involving dynamic recognition of the substrate during the whole translocation process. Supramolecular chemists, taking inspiration by the natural anion transporters, have designed artificial systems able to mimic, at the functional level, several features of the natural ion channels. The scope of this research is twofold: on one hand to get insight on the molecular basis of recognition and transport, and on the other hand to get control of the biomedical relevant processes. The present review focuses on the synthetic systems promoting anion transport, covering both artificial channels and carriers that operate in phospholipid membrane. The design principles of such systems will be discussed together with the potential biomedical applications.