1680s, "to bring something to a shop, to expose for sale," from shop (n.). The meaning "to visit shops for the purpose of examining or purchasing goods" is first attested 1764. Related: Shopped; shopping. Shop around is from 1922. Shopping cart is recorded from 1956; shopping list first attested 1913; transferred and figurative use is from 1959.
1764, "act or practice of visiting shops," verbal noun from shop (v.). Meaning "goods that have been purchased" is from 1934. Shopping bag attested from 1886; shopping list from 1913.