Surface-to-underwater missile is more a way to categorize than a widely used term for specific weapons. There have been two broad classes, one of which has become obsolete with the disappearance of tactical nuclear weapons at sea. The other is a multiple-stage precision-guided munition; the first stage does not need high precision, but delivers an intelligent torpedo to the general area of the target, where the torpedo does the bulk of guidance.
Examples of current boosted torpedoes include the Russian RPK-2 Viyuga (NATO designation SS-N-15 STARFISH) and U.S. RUM-139 Vertical Launch ASROC. They reflect a rethinking of the role of antisubmarine torpedoes on surface ships. Since submarine-launched torpedoes have a range much greater than those of warships, warships began to take on the role of sensor and support platforms for helicopters, which would localize the submarine at a range safe for the warship, and drop a lightweight homing torpedo.
In blue-water operations, if the surface vessel used deck-mounted torpedoes at all, it would be as a final act of defiance hoping to hit the submarine that had launched the heavy torpedoes that would soon hit the warship. There may still be a role, however, for ship-launched antisubmarine torpedoes in littoral operations, where the engagement may be at very short range with a submarine rising from the sea floor. Even then, a boosted torpedo may be able to hit the submarine before it can launch, given the reality that a rocket-assisted torpedo moves much faster in the air than does an underwater torpedo.
Even in blue-water operations, what if weather prevents helicopter operations, or the helicopter is on a mission or otherwise unavailable? Rocket-boosted torpedoes give the surface ship an opportunity for survivable engagements without helicopter assistance.