Tank destroyers cover a very specialised catagory of armored vehicles, that, as you might guess, are made to destroy tanks or, more correctly, other armored vehicles. Generally, if it's not made of meat or sand and is on the ground, you can use a tank destroyer against it. Note that deployed guns are made of sand, so defencive positions are safe.
Some units will be called Tank destroyers even if they are assult guns in nature. This will be because they are really bad at the other role, so bad it rarely comes into play - just don't be shocked if some master player will suddently attack your infantry with a tank destroyer.
Most factions have mobile versions of their deployable AT weapons. They cost more (usually around double cost) and are armored targets that cannot be pinned, but can be targetted by other tank destroyers and AT guns. The primary use for TD's is obvious: destroy enemy armor. Excact use of these weapons vary based on facion an type, as the costs range from 1400 to 9000 with obviously different approaches to using them.
Using tank destroyers is not as efficient, as one may think at first. The main benefit of tank destroyers is the faster deployment speed compared to tanks, as the factory will cost less then a tank factroy in every case. Of course, tank destroyers are cheaper then actual tanks, but the cost difference is usually outweighed by the wider applications of tanks.
Tank destroyers are usually much easier to control, as they ignore infantry completely, but they cannot blind fire their weapon, like tanks and assult guns. Most tank destroyers lack a turret as well - it's up to the players play style to decide if this is beneficial or not.
The wolverine takes it's place as one of the cheapest TD's in the game, while also being very useful to have around. Losing one doesn't slow down the US player at all - you need to take out at least four for him to notice they aren't working as well as he intended. The drawback, of course, is the damage of the gun itself. Essentially the same 3-inch you can find in the towed gun yard, it tends to suffer less from innacuracies and more from simple late game armor values. It does get a nifty AA machine gun though, so no matter what you do, you're bound to have some anti-air protection be it with Shermans or wolverines.
GBR Achillies and AEC
Similar to the Wolverine in every aspect except crappiness - it's not. Like the wolverine, the 17 pounder is insanely cheap, has a turret and average armor, but since it uses the GBR AT gun mounted on treads, it has great penetration, serving reliably untill the very late stages of the game, when, unfortunatly, bigger (yes, even bigger) weapons must be made.
The AEC is similar to the marder in the sence that it's cheap and has little armor, but it does have a turret and is much faster. Much cheaper then the Achillies, it stands closer to the wolverine and marder, but is somewhat less effective. It is, however, the fastest way to bring low-level AT weaponry over long distances, as it is a car, after all.
Soviet SU-85 and SU-100
Marking the size of the gun their using, the SU seires handle in almost the exact same way, being a moderatly armored tracked turretless tank destroyer from the towed gun yard with the tank destroyer modification. The cost difference is about double: 3500 for the SU-85 and over 6000 for the SU-100. The SU-85 allowes to just barely not die from enemy tanks, which tipically arrive much earlier then yours. It's speed even allowes it to chase down bold tanks that go deep into your teritory. The SU-85 can take on any medium tank quite comfortably, as it's front armor is close to that of late game upgraded mediums.
The SU-85 quickly becomes outdated, despite it's relativly powerful weapon, since being generally less manuverable then tanks, anything that doesn't blowup in a single well placed shot will become a serious threat. Fortunatly, you can sacrifice a third of the fireing speed in return for a bigger gun. In case you really want to explain why tanks are not allowed in a particular portion of the map, you show your middle finger - the SU-100. Impressive range and firepower, a monster tank destroyer that is comparable only to the ISU-152 in tank destroying performance, but does so at a much safer distance and with much cheaper ammunition? as well as bringing faster, more consistent results. A small squad of SU-100 is hard to get and easy to lose, but you can be sure you won't be seeing enemy armor anywere close to them, as even 100mm of front armor might not be enough to live after a single shot fired. The SU series continues the soviet characteristic of having very, very fast projectiles and they will only miss at maximum range on certain occasions, as the SU-100 will fire from hidden portions of the map for most of the time, making it's trajectory somewhat difficult to predict.
German Marder, Jagdpanzer IV/70(V) and Jagdpanther
The marder is the earilest TD on the field and stays around until tanks start breeding like rabbits. Dies to almost anything, but has a very powerful anti-tank weapon, just like the Pak40. Being the cheapest Tank destroyer in the game, you can't really complain about lack of armor or turret, as you can get it before the notion of armor becomes known to the enemy at all. Losing weapons like this is more punishing then usual, as they are mostly made in the early stages of the game, when command is valuable.
The Jagdpanzer's and Jagdpanther's are both expencive, with the Jagdpanther costing upwards of 9000 command, enough for several medium tanks or a anti-tank sortie to be destroyed in the process of sniping this beast (let that sink in for a moment - the enemy can lose a whole anti tank squad and still make a profit if they destroy just one of these). The Jagdpanzer's are well balanced anti tank solutions for mid-late game armor. They are somewhat inefficient, but not enough for anyone not to use them when they need to. The Jagdpanther is rarely seen and not just because getting one is a feat - it just fires so far behind the lines you never get close enough. For all those of you who like big things, this tank destroyer will surely raise your ego to new levels, letting everybody on the map know that you are a big boy that can handle oversized weaponry from distances even binoculars cannot reach.
Italian Autocannone da 90/56, Semovente da 47/32, Semovente da 75/18, Semovente da 75/46 and Semovente da 90/53
A somewhat hard to use, but suprisingly powerful AT gun, the autocannone has great range and impressive penetration. Being a rather heavy truck, it suffers from lack of armor, as a couple of well places shots from larger weapons will take your toy away from you. In return, making them is pretty cheap and a fully rotatable turret removes the need for constant managment. The drawback is it's inability to fire while moving. Due to Italy's general lack of proper AT, some players will rush to the autocannone as it's not too hard to get and other options in the tree will not leave you in a terrible position, either.
Now if you're thinking anything called a Semovente is an AT gun on tracks, you're mistaken - some are also assult guns. Even some listed here can function as anti-infantry weapons if needed, but that's not their proper use. Varying in size, cost and power, the different semovente's share a few traits: lack of a turret and difficulty of use. Unlike most turretless tank destroyers, the Semovente cannot aim it's weapon at all, making it more clumsy in close combat situations. Some models are eqipped with HEAT round to be fired at closer ranges, mostly to compensate their instant death scenario if anything actually gets close, but in most cases, they are just barely out of range to use it.
A general guidline to distinguish the different Semoventi is to check the cost, as funcionally (and even in appearence) they are the same.
Japaniese Ho Ni iii
Like all japaniese armor, the Ho Ni has almost none of the armor that other TD's can show off. Also unlike other tank destroyers, it's weapon if relativly weak as well - even weaker then the Wolverine's gun when it comes to penetration. It's advantage is, like most Japanise tanks, it's low cost at around 2000. It has a relativly fast reload, so if you get in close with another tank, you will likely take it out unless it has friends.