When the US and USSR started developing nuclear torpedoes, what did those respective navies see as the use-case for them?
Does the US or Russia or anyone else still deploy them? Have technical advancements in conventional torpedo guidance, target acquisition, etc. covered the space nuclear torpedoes were meant to fill?
Nuclear torpedoes were primarily developed to counteract the limited accuracy of early homing torpedoes - the increased blast radius meant that a near-miss would still do significant damage. Nuclear torpedoes would also do significant damage against hard targets with only a single hit.
The idea of a nuclear torpedo first came about in 1943. Captain William Parsons, the US Navy officer who led the Manhattan Project's ordnance division, suggested developing a nuclear warhead capable of fitting onto the Mark 13 torpedo. Oddly, and unlike most future developments, this was an aircraft-carried torpedo. The Mark 13 was the main anti-shipping weapon of the US Navy's torpedo bombers, indicating that Parsons was thinking primarily in terms of use against surface ships rather than subs. The idea was opposed by Parson's superiors within the Manhattan Project, as the project was heavily stressed with producing a device capable of fitting in a B-29, let alone the small aerial torpedo - and there was, at the time, little evidence that the bomb would be an effective weapon against ships. The Soviets began developing their nuclear torpedoes in 1949-50, with two weapons being planned. One was a large land-attack weapon, the T-15 (of which more later), while the other was the T-5, a 21in anti-ship/submarine torpedo. This used a 10kt warhead, designated RDS-9. An initial, land-based, test was a failure, but later tests on the Novaya Zemlya underwater range were more successful. The T-5 would enter service in 1958, as the Type 53-58 torpedo. It was an unguided torpedo, intended for use against surface ships and diesel-electric submarines running on or near the surface.
Meanwhile, the USN was making its own developments. It had introduced a new heavyweight, acoustic-homing ASW/anti-surface torpedo in the Mark 37 in 1956 - and added wire guidance the next year. Unfortunately, this was a slow torpedo, capable of just 14.7 knots when wire-guided. This had been seen as acceptable when it was in development as the likely targets were slow diesel-electric submarines. However, the year before it entered service, the USN had launched its first nuclear submarine, the Nautilus. This was capable of reaching and sustaining speeds that would let it outrun the Mark 37. A Soviet equivalent would have similar capabilities. There were also worries that the Soviets were developing submarines that could dive deeper than previous. These might have thick enough pressure hulls to keep out smaller conventional warheads. To counteract these threats, the USN began developing the Mark 45 ASTOR (Anti-Submarine Torpedo) for use on its submarines. This had a 20kt warhead, was capable of 45 knots and had a range of 15,000 yards. It was wire-guided, and unusually was command-detonated by a signal sent down the wire, rather than relying on a conventional exploder. It was an effective ASW weapon, but did not inspire confidence in the crews who had to use it. There was a grim joke that it was the only weapon with a pK (probability of scoring a kill) of 2 - the target submarine, and the submarine that launched it. ASTOR entered service in 1960, and was the only NATO nuclear torpedo. It would exit service in 1976, following the development of the Mark 48 torpedo. The Mark 48 was a fast, long-ranged, heavy-weight torpedo with excellent ASW sensors and a relatively conventional large warhead, completely removing the need for ASTOR.
Meanwhile, the Soviets were making their own developments. From 1962, they began to place the ABS-30 warhead aboard their submarines. This was a nuclear warhead that could be fitted, at sea, to any Soviet 21in torpedo. As such, it could be fitted to both acoustic anti-submarine torpedoes, or anti-surface weapons, either non-guided or wake-homing. Two ABS-30s were carried by each Soviet submarine until more typical weapons could enter service. These would come out in 1973, after the Soviets introduced their larger 650mm (25.6in) torpedo tubes. The Type 65-73 was an unguided, high-speed long-range torpedo with a nuclear warhead. It was intended for use against NATO aircraft carriers, able to kill them in a single hit. It was also seen as being capable of being used against coastal targets, if necessary. The following Type 65-76 of 1976 added a wake-homing facility and may have been able to carry a nuclear warhead. Finally, the VA-111 'Shkval' rocket torpedo was developed from 1960, and entered service in 1977. Shkval was a last-ditch anti-submarine weapon, capable of speeds up to 200 knots thanks to a system that uses the rocket's exhaust to create a shell of bubbles around the torpedo. However, this meant that it could not use acoustic guidance, so a nuclear warhead was needed to give sufficient accuracy. The intended use case for Shkval was for it to be launched down the bearing of an incoming torpedo, to take out the attacking submarine before the incoming torpedo could impact. The downfall for the Soviet nuclear torpedoes was a series of agreements in 1991. These agreements, the Presidential Nuclear Initiatives, aimed at reducing the number of tactical warheads in service. Under them, Soviet/Russian nuclear torpedoes were removed from submarines, and held in centralised facilities, making it harder to use them at a moment's notice.
This has mostly covered the tactical uses of nuclear torpedoes, but there was also some interest in their uses against strategic targets. In the days before ballistic or cruise missiles, a nuclear torpedo could allow a submarine to attack a defended harbour, port or coastal city - and as already noted, the Type 65-73 could be used in this role. In the immediate period following WWII, there was some interest in the USN in a torpedo that could be used against harbours. Preliminary research was done, but this was not taken further. The Soviets took the idea further, with the T-15, designed to attack major naval bases like Gibraltar or Pearl Harbor. This was to be a massive weapon, with a diameter of 1.55m. Propelled by electric motors, it would have a range of 30km at a speed of 30 knots. The weapon was to have a specially designed carrier submarine, the Project 627, which would have a single forward-facing tube for it, as well as two 21-inch tubes for self defence. Project 627 was to be the first Soviet nuclear-powered submarine. Initial construction work began at the Molotovsk shipyard in September 1955. However, the project faced significant opposition from the Soviet Navy, who felt that it was not what they needed. Shortly after it was laid down, the design was changed to a more conventional design, which would become the November-class SSNs. With this, the T-15 was dropped. The idea does, however, seem to have been resurrected, with the recent Russian development of the Poseidon strategic torpedo.