Parts 1, 2, and 3)
Air defense weaponry fell into five basic categories: Airborne interceptors, long-range missiles, medium-range missiles, short-range missiles, and point defense. Let's consider each in turn.
Airborne interceptors were basically the Combat Air Patrol, launched from the carrier. CAP could be airborne, or ready on deck in various alert states. Ready 5 would have the aircrew sitting in the aircraft, hooked up to the catapult and with the engines turning. In Ready 15, the engines were shut down. Ready 30 would have the crew outside of the aircraft and the aircraft near the catapult. Ready 45 and Ready 60 would have the crew in the ready room below decks.
The king of the airborne interceptors was the F-14 Tomcat. The Tomcat carried a powerful radar system, the AWG-9, and the Phoenix missile.
The Phoenix was a serious long-range AAW weapon. Given that the F-14 might have been flying a few hundred miles from the carrier battlegroup and then that the Phoenix itself had a range of something on the order of a hundred miles or so, the F-14/Phoenix weapon system had the capability to engage Soviet Naval Aviation cruise-missile shooters before they reached firing range.
Phoenix's main limitation was that it was not a dogfighting missile, it was a missile that made the F-14 into a flying guided-missile ship. Phoenix was designed for a general hot war, where the only aircraft in the sky would be Ours, Theirs, and Civilians Stupid Enough to Fly Through a War Zone. It was not designed for a limited-war environment where the rules of engagement required visual target identification. Phoenix could only be carried by F-14s, so once the F-14s were retired, so was the Phoenix missile.
Talos was the first long-range shipboard AAW missile.
Talos was a monster in its size. The missile itself was not a rocket, it was powered by a ramjet. It was akin to firing an unmanned aircraft at a target, as the missile weighed something like 7,000lbs and was 35 feet long (give or take). Originally, Talos had a range of 50 nautical miles, the later versions doubled that. The warhead was either continuous rod or nuclear. Talos was so huge that ships carried them both ready to use and, to save space, more missiles were unmated, with the booster, the sustainer and the warheads all separated.
Only one ship, the USS Long Beach, was purpose-built to fire Talos; it was also the only one to shoot them during wartime at a live target (two North Vietnamese MiGs). All the other Talos shooters were rebuilt heavy-gun cruisers from World War II. They were ugly ships; the missiles came out from the deckhouse onto a launcher sited where the first 8" gun turret had been. The missile radars were where the superfiring gun turret had been.
Talos was retired around 1980 as were all of the Talos shooters except Long Beach. She was converted to fire Terriers. The Talos missiles left in inventory were converted into flying targets and all were eventually used up for that duty.
Terrier started out as a medium-range missile, with a maximum range of 20nm. It was, like Talos, a two-stage weapon, but the second stage was powered by a rocket motor. Terrier was also a large weapon, but nowhere near as large as Talos. It was employed by DLGs, which, in 1975, were redesignated as either DDGs or CGs. The warhead was either continuous rod or nuclear, though unlike Talos, the weapons were carried assembled.
To save space, though, the fins were not added to the missiles until they were on the rail in the missile house behind the launcher.
Tartar was a short-range single-stage rocket, basically the front half of a Terrier. It was fired from Adams class DDGs, Brooke class FFGs, and Perry Class FFGs.
Some Knox class FFs had two Tartars in their ASROC launcher box. Tartar had a range of 10nm or so and only had a continuous rod warhead.
Talos, Terrier and Tarter were sometimes referred to as "the T-birds". All functioned about the same way: They rode a beam towards the target and then homed in from the radar reflections as the ship's missile illumination radar shined on the target ("semi-active homing"). They were always "tail-chasing" the target; they were flying towards where the target just had been. Range against a crossing-target was piss-poor. Worse, the ships could only have as many missiles in flight as they had radars.
Terrier was replaced by the SM-1/2ER missiles, Tartar by the SM-1/2MR missiles, though the ships that used them were still referred to as "Terrier ships" or "Tartar ships". The Standard missiles did away with beam-riding, instead steering the missiles towards their target by a datalink that could predict an intercept position and fly the missiles there, using semi-active homing for terminal guidance. That, along with better rocket motors and more powerful boosters for the ER series greatly increased the range of the missiles. The datalink system also permitted the ships to have many missiles in flight at one time per fire-control radar system. The latest models of SM-2MR have a range almost the same as the later models of Talos, while the SM-2ER can fly even further.
There was concern that at some firing angles, the SM-2ER booster could erode the ship's deck, but I do not know if it was ever addressed. During the late 1980s and early 1990s, the steam-powered Terrier ships were given a "New Threat Upgrade" to their missile systems in overhauls that cost over $50 million each to permit them to employ the then-latest variants of SM-2ER. Unfortunately, the Cold War ended soon after the NTU upgrades were put in service and the steam-powered Terrier ships were almost immediately retired.
All of the steam-powered Terrier and Tartar ships have since been scrapped or sunk. The fucking Navy couldn't be bothered to save a single one as a museum ship to the Cold War.
 All this is from old memory, so if I'm wrong, meh.
 The latter two groups you could shoot at.
 During the reign of the Shah, Iran purchased F-14s and Phoenix missiles. They may still have some missiles left.
 SM-3ER is designed for ballistic missile defense. This is why.
 The Adams-class DDGs were also all scrapped or sunk. Only the German Navy, which had three built here (and customized to their own needs), saved one. The Navy saved numerous ships from WW2, but only the USS Barry and the USS Nautilus, which is historic in its own right as the world's first nuclear sub, were spared.