Manhwa (also romanized manwha) are Korean comics, which read left-to-right. Manhwa and manga are the same word (same kanji), they simply have a different pronounciation in Korea and Japan. Korean and Japanese comics are very similar, with girls' (soonjung) and boys' manhwa, but they each have their own unique feel due to stylistic and cultural differences. Learn more about the differences between manhwa and manga at Sequential Tart and Manga Life. Korean manhwa are also more creator-driven than Japanese manga, which are heavily shaped by editors.
Although the first girls' manhwa (I.N.V.U.) was published in English in 2002, the number of series in English remains small compared to the influx of manga. This is largely because the Korean comic market is suffering a recession due to the manhwa rentals who, until recently, did not pay any royalties to publishers. Additionally, the first two publishers to attempt publishing manhwa in a big way (ADV Manga and CPM Press) have had serious financial difficulties, resulting in the cancellation of many series. Fortunately a number of new publishers have stepped up to offer a variety of manhwa: ICE Kunion, Netcomics, and Infinity Studios. (Unfortunately the translations of the Korean publishers - Netcomcis especially - tend to fall far below normal standards.)
Rated Teen unless otherwise indicated. Ongoing titles indicated by +
DramaQueen is a small specialty publisher known for their high production values and dedication to the BL market, in addition to some very interesting girls' manhwa and manga. From their About Us page it sounds like DramaQueen is an amateur group turned professional publisher, which is just too cool because, not only are they the first female fan-run publisher, their books are some of the best in the business in terms of production value. DramaQueen is primarily a BL publisher, but they've quickly expanded into shoujo romance from both Japan and Korea. Due to the graphic nature of their BL books, they are not (currently) distributed in bookstores and are available online thru their website, RightStuf, Amazon, and Barnes & Noble.
Ice Kunion is new publisher which debuted in 2005. Unlike most manga publishers which are American based, Ice Kunion is a consortium of Korean publishers which banded together to create an American imprint to bring their titles directly to the American market. (See the 2005 ICv2 interview). Their books are large sized and have nice shiny covers, but the inside print quality can be disappointing and their translations are not up to the quality of American publishers (but they're better than Netcomics). They have an interesting range of titles and publish girl's series nearly exclusively. Also, since the properties are all owned by them, they have the rights to the extra materials that were in the original anthologies and can include those in their books.
I've been able to find out very little about this new American-based publisher. They have very little web presence and provide few details on who they are, apart from their hype-filled press releases. Infinity Studios debuted in late 2004 with one series, the male-oriented Peigenz. In 2005 they began publishing a small handful of titles, including girls' manhwa. Publishing is been sporadic, with many months between volumes. The good news is, they put a lot of effort into production quality and have some of the best looking books: numerous glossy colour pages, nice dust jackets, excellent print quality. Reviews at AnimeOnDVD have noted numerous scattered grammatical errors, otherwise translation quality seems good.
Tokyopop was the first American publisher to try publishing manhwa, and they have both great titles and mediocre ones (more of the latter). Their process for acquiring manhwa is, unlike their manga, haphazard and mostly based on the suggestions of the publishers. But their translations are certainly far better than the Korean publishers, since they have better editors.
Netcomics is the American branch of the Korean manga publisher eComix, which publishes comic book contents as online books, mobile phone contents, along with printed books. Netcomics similarly provides their manhwa/manga in both an online pay-per-view service and regular print versions. Series debut online before being compiled into print volumes, and can be viewed for fraction of the cost of a print book: the first chapter of a book is free and the rest of the book can be read online (but not downloaded) for a charge of 25¢ per chapter. Unfortunately their translations range from "okay" to unreadable, so you really should preview them first. The titles themselves are often quite good and different from the usual fair, but they seem to very poor editors =P Hopefully this will improve as the company matures.
ADV Manga launched a new publishing division for manga and manhwa (mostly manhwa) in 2003 with a very ambitious plan for growth. They licensed entire catalogs of titles and released a few first volumes of a bunch of series, but soon after cancelled most of them due to financial problems. CPM Press, a long running but small manga publishing arm of Central Park Media, has also suffered severe financial setbacks and their manga publishing has all but ceased.