Kantai Collection

Kantai Collection ("Fleet Collection", a.k.a. KanColle) is a Japanese browser-based Card Battle Game by Kadokawa Games, in which the player is an admiral managing a fleet of Moe Anthropomorphized warships from World War II.

The task of these "fleet girls" (kanmusu, also translated as "shipgirls") is to fight the mysterious "Abyssals", a fleet of (what appear to be) corrupted fleet girls and sea monsters who have driven humanity back from the sea.

The admiral's job is to direct their operations, supplies, and repairs, and somehow find time to manage the furniture and marry one of the fleet girls (or more than one).

The game itself is pretty thin on story and background, but there are multiple spin-off mangas and a Twelve-Episode Anime (plus a movie) set in its world (or worlds based on its central concept, anyway).

"Sendai: You need to think a little about how she feels."
 * Bribing Your Way to Victory: Most resources can be obtained in-game by sending the fleet out on missions, but they can also be purchased instantly in the shop.
 * Buxom Is Better: Bust size (and overall age) seems to correlate with ship class and firepower. Destroyers look middle- to high-school aged, cruisers high-school aged or recently graduated, and the battleships start 'mature' and go from there -- compare the fast-battleship Kongou to super-battleship Yamato...
 * Canon Fodder: What are Fleet Girls? How do they fight?  Where do they come from?  Are they the spirits of the warships themselves, summoned from some 'ship afterlife', or are they regular human girls or women who are somehow found to be 'reincarnations' of these ships?  How are they related to Abyssals?  The game itself is silent on the details, and while several spinoff media have contradictory views on it, Kadokawa have not endorsed one over the other.
 * The opening narration of the anime adaptation indicates that fleet girls are born human and somehow obtain the spirits of the warships later.   Fleet girls and Abyssals fight on the surface of the water (appearing to "skate"), and carrier girls launch their airplanes by firing their ranged weapons (e.g. shooting an arrow which turns into a wing of aircraft).
 * In the manga KanColle: Someday as the Seas turn Calm, the fleet girls skate as they do in the anime, but aircraft are launched 'conventionally' from their flight decks.
 * In the manga KanColle: Bonds of the Wings of Cranes, fleet girls are the reincarnations of warships, summoned (essentially) from the moment of their sinking.
 * Some of the 'one-shot' manga anthologies depict fleet girls as being warship-sized giants!
 * Creator Provincialism: Of course, most of the ships are Japanese, and many of the seasonal events are based on campaigns from the Pacific Front of WWII (which raises some hackles in other countries...).
 * Friendly Fandoms: With Arpeggio of Blue Steel (the Winter 2013 event included several characters from the anime adaptation Arpeggio of Blue Steel -Ars Nova-) and World of Warships (there's more than a few players who get Japanese warships because of this game or its anime adaptation, and players who use them are likely to encounter catchphrases from the anime in chat).
 * Historical In-Joke: Lots of the girls' quirks are based on their service or history. For example, Kongou was built in England (and then rebuilt in Japan), and so has an affinity for tea and often sprinkles her speech with Gratuitous English.
 * Level Up At Intimacy 5: Marrying a fleet girl lifts her level cap from 99 to 155, reduces her fuel and ammo consumption, and improves several of her minor stats (e.g. luck, evasion, and scouting).
 * More Friends, More Benefits: There's no limit to how many partners an admiral can have (although each ring after the first costs real money).
 * Moe Anthropomorphism: The fleet girls appear to be human, but wear "rigging" which bears features of their 'ship-selves' (e.g. smokestacks and turrets). Other major accessories or distinctive features may be worn (e.g. headbands with distinctive radar masts or antennas) or carried (e.g. flight decks).
 * Politically-Correct History: To be fair to Kadokawa Games, most of the atrocities of World War II were committed by civilian governments or ground forces, rather than navies. However, the inclusion of the submarine I-8 (whose crew did commit war crimes) raised more than a few eyebrows overseas, as do the seasonal events which revolve around recreating historical or planned (Japanese) naval campaigns of World War II.
 * Voices Are Mental: Averted. In the "Hiei's Curry" radio drama, Maya switches the Kongou sisters' headbands around while they're in the showers, and while they swap mannerisms when they come out and put them on, their voices stay the same.
 * What the Hell, Hero?: In the anime, Fubuki pushes herself almost to the point of destruction, hoping to impress her admiral (who had previously put her into an oddball mixed fleet, and then broken it up once she got it into shape) and earn her remodel. She is almost fatally destroyed in battle, but barely survives.  When she wakes up, with Mutsuki tearfully embracing her, her first question is whether her final attack had hit the Abyssal she had (almost fatally) charged.  Mutsuki shouts at her to take better care of herself, and flees crying.  Sendai comments disapprovingly: