At the Fall of Númenor, Elendil bore the Palantíri to Middle-earth, and placed them throughout his realm. The chief was set in the Dome of Stars in the city of Osgiliath. The others were placed in Minas Anor (Tirith), Minas Ithil, Orthanc, Amon Sûl, Annúminas (the first capital of Arnor), and Elostirion (in the Tower Hills of Eriador).
After Elendil's death, the Eldar took the Palantír of the Tower Hills back, which saw only into the West, so that Elves often made pilgrimages to view Valinor. It later passed to Valinor with the Last Company of Ring Bearers in 3021 of the Third Age. The Stones of Amon Sûl and Annúminas were taken and kept at Fornost, but were lost in the shipwreck that killed Arevdui.
The Stone of Osgiliath was lost in the great civil war of Gondor, the Kin-Strife, for the city was burned. In 2002 of the Third Age, when Minas Ithil was siezed by the Nazgûl, and converted to Minas Morgul, Sauron's minions took control of that stone, and gained a power over the rest. Saruman took the Stone of Orthanc in 2759, but was immediately ensared by Sauron, and the Minas Anor Stone soon became dangerous to use, due to its relation to the Ithil-stone. Indeed, Sauron manipulated Lord Denethor II's visions, and eventually turned him to darkness, and even suicide. After this, all that could be viewed by the use of the Stone, was an image of two burning hands, unless the Holder posessed the strongest of wills.
The Orthanc-stone was recovered by Aragorn near the end of the War of the Ring, after being cast out of the tower by Wormtongue. He used it, being strong willed, to his advangtage, and learned of many things, including the sailing fleet at the Corsairs, which led to victory at the Pelennor Fields.
What became of the Seeing-Stones since the days of Aragorn is not known.