Battleships
Battleships ("BSs", sometimes "BBs" from US Navy terminology) are the biggest, heaviest sub-capital combat ships in the game. They are correspondingly expensive, with even the cheapest battleship hulls selling for many tens of millions of ISK. Tech 1 battleships are standard tools in PvP and PvE combat. There are two classes of Tech 2 battleships: Marauders, which are specialised for mission-running, and Black Ops battleships, which can transport fleets of stealthy ships across long distances using covert cynosural fields.
T1 Battleships
In PvP Tech 1 battleships can mount great buffer tanks and can deal very high dps when fitted for short ranges. When mounting long-range 'sniper' fits, battleships can fight at the very longest ranges possible in Eve's engine, while still dealing effective DPS. Such sniper-fit battleships -- commonly the Apocalypse, Megathron, Maelstrom, Tempest and Rokh -- are often the backbone of fleets used to fight for territory in nullsec. One battleship is something of an exception: the Caldari Scorpion, with its bonuses for ECM, is the only Tech 1 electronic warfare battleship.
Battleships' weaknesses are low speed and agility, combined with slow locking speeds and poor gun tracking speeds. Battleships therefore struggle to force smaller ships to engage, and to kill smaller ships even when they can be pinned down.
In PvE battleships are also the standard class of ship used to run Level 4 missions solo, since they can fit active tanks good enough to survive lots of DPS over a sustained period of time, while still dealing out enough damage to complete missions reasonably quickly. Battleships fitted to solo Level 4 missions usually rely on light and medium drones for defence against smaller NPC targets.
Amarr:
- Abaddon: Monstrous tank and decent damage. A beast.
- Apocalypse: Sniper.
- Armageddon: Its name says it all. Huge DPS, can have a sickening buffer tank, good remote repair platform, controls five heavy drones. Very nasty.
Caldari:
- Raven: Missile ship. Most effective Caldari BS for most situations. Usually heavily tanked. Standard PvE L4 mission-running BS.
- Rokh: Caldari sniper. Longest range in the game, when properly fit. Can still be nasty with a good blaster fit at close range.
- Scorpion: ECM boat, low DPS. Can shut targets down from 150KM; sometimes armor tanks; good in remote-repair gangs. Not a solo boat. Frequently primaried.
Gallente:
- Megathron: Sickening amount of DPS at close range. Also used as a sniper. A solid primary when calling BS primaries.
- Hyperion Close-range blaster gunboat with an active armour tank bonus. Offers little benefit over the Megathron for PvP.
- Dominix: Drone boat. Versatile; lots of grid/cpu/cap. Good for remote repairing allies or neuting enemies. With multiple flights of T2 sentry or heavy drones, can also do a lot of damage. Standard L4-running Gallente BS.
Minmatar:
- Tempest: High DPS, gank over tank. Good RR or sniper, or fitted for speed as 'Eve's largest battlecruiser'.
- Typhoon: Very versatile, can be used for almost anything. Quite dangerous with a pilot with a lot of skillpoints. Can control five heavy drones.
- Maelstrom Also used as a sniper. Standard PvE L4 mission-running BS. Strong active shield tank.
T2 Battleships
Marauders
Marauders are essentially designed to run missions efficiently. They mount half as many weapons as their Tech 1 equivalents, but have damage bonuses that let them deal at least as much DPS. The spare highslots are usually dedicated to tractor beams and salvagers, so that mission-runners can salvage as they go. Marauders come with tractor beam bonuses to help salvaging, and the Amarr Paladin and Gallente Kronos also have webbing bonuses which can help pilots to kill small targets.
These are not very useful in PvP. They have very low sensor strength, making them very easy to jam, and their active-tanking abilities are less useful in PvP, which usually favours buffer tanks. The Paladin and Kronos's webbing bonuses might be useful, but Blood Raider and Serpentis ships get similarly effective webbing bonuses and cost less (even though they're pirate ships).
Black Ops
These are the big brothers of the Recon Tech 2 cruisers. However, while they do get bonuses to how fast they move while cloaked (which actually means that they'll move faster when cloaked than when not cloaked with the Black Ops skill at a decent level), they can't warp while cloaked. Black Ops battleships cost about 700 million ISK before fittings, so it's rarely worth risking them in combat. Their primary role is to provide covert jump bridges.
Covert cyno fields can now be lit even in cyno-jammed 0.0 systems and don't appear as a beacon in the entire system like a normal cyno. Black Ops battleships can lock onto these fields and create bridges to them, which then allows other covert ops ships -- any ship that get a bonus to cloaking, including Tech 3 cruisers with the cloaking subsystem -- to jump in.
Black Ops battleships don't really have a PvE application.
Faction Battleships
Faction BSs, like other faction ships, are traded through contracts rather than on the market. They usually cost several hundred million ISK.
The 'Navy Issue' or 'Fleet Issue' battleships are, with the exception of the Scorpion Navy Issue, souped-up versions of the normal BS, with extra slots, more hitpoints &c.
The pirate faction battleships are more unique, requiring two races' BS piloting skills and bringing unusual tactical combinations to the table.
- Armageddon Navy Issue
- Bhaalgorn -- Tough and powerful capacitor warfare platform. Not much use in PvE.
- Machariel -- Incredibly fast and agile (for a BS), and capable of dealing lots of damage. Popular for PvP, and for PvE, where it rivals the Vargur's mission completion speed.
- Megathron Navy Issue
- Nightmare -- Good laser platform. Can combine shield-tanking with lasers.
- Rattlesnake -- Caldari-style shield-tanking, Gallente-style drone bonuses. The only BS that can mount a really effective passive shield tank for PvE.
- Raven Navy Issue -- Popular for blitzing missions as fast or faster than a Golem (but not as good for salvaging).
- Scorpion Navy Issue -- Not an ECM boat like the Scorpion. Like a Raven with a tougher tank but weaker damage-dealing capabilities.
- Tempest Fleet Issue
- Typhoon Fleet Issue
- Vindicator -- Popular blaster platform, as the webbing bonus helps it force its targets into blaster range.