Multiphasic shields were an advanced type of deflector shield technology, used by the Federation in the 24th century, capable of protecting a vessel from subspace radiation and the dangerous energy emissions generated by stars.
According to Captain Kathryn Janeway, the fact that Starfleet ships were equipped with this technology was taken for granted in the year 2373, while in the year 2293, multiphasic shielding was not yet in use and the technology was still in the early stages of development. (VOY: "Flashback")
In 2374, after the USS Voyager's sensors detected the Omega molecule in the Delta Quadrant, Captain Kathryn Janeway ordered multiphasic shielding installed around Voyager's warp core, in accordance with the Omega Directive. (VOY: "The Omega Directive")
In 2376, Ensign Tom Paris came into possession of a shuttle, which he named "Alice," equipped with multiphasic shielding. This shielding made it impossible for the Voyager crew to beam Paris off of the shuttle, when use of the ship's neurogenic interface caused him to display irrational and dangerous behavior. (VOY: "Alice")
In 2377, DaiMon Nunk fantasized about buying a ship with multiphasic shielding and a gold-pressed latinum hull after selling Seven of Nine's nanoprobes. (VOY: "Inside Man")
According to the novelization of The Search, the USS Defiant was equipped with multiphasic shield generators.
In 2401, the USS Stargazer and presumably the Sagan-class as a whole utilized multiphasic shielding. The Stargazer employed it while investigating the spatial anomaly that the Singularity emerged from. (PIC: "The Star Gazer")