I'm embarrassed to say that though I write regularly about TV and Movies and consider myself pretty well-informed about all there is to know about the industry, I am completely out of the loop regarding Anime.
So...I found this "History of Anime" article from Variety to be quite informative, including a handy timeline, reproduced here:
"Astro Boy" series starts in Japan, launches in the U.S. later the same year. The original manga was created by Osamu Tezuka, who is considered the father of the format.
-"Gigantor" series debuts in the U.S.
-Another of Tezuka's creations, "Kimba the White Lion," launches.
-"Speed Racer" takes off in the U.S. a year after it was first broadcast in Japan. MTV picks up the show in 1993; Cartoon Network adds it to their lineup in 1996.
-In the same year, restrictions over violent content limit Americans' access to Japanese animation, including such shows as "Devilman."
-"Battle of the Planets'" (aka Gatchaman) and "Star Blazers" series debut in the U.S.
-"Voltron" hits U.S. shores, followed by "Transformers." Both the anime and tie-in toys become popular.
-"Robotech" takes off in the U.S.
-An animated "Transformers" feature earns more than $5 million at the box office.
-Anime feature "Akira" opens.
-Hayao Miyazaki's "Castle in the Sky" receives a limited released in the U.S.
-Troma releases a dubbed version of Miyazaki's "My Neighbour Totoro" in the U.S. Variety critic Leonard Klady says he doesn't get it.
-Many Japanese animations go directly to video, where more mature titles with sex and violence catch on among cult audiences.
-Video rental stores start to set up Japanese anime sections.
-The word "manga" enters the English language with "pop, erotic, futuristic and artistic" connotations.
-"Sailor Moon" airs in the US, helping to expand the image of anime from being a male-oriented media to something both sexes can enjoy.
-The Japanese trend of dressing up as anime characters (or cosplay) comes to the U.S.
-"Ghost in the Shell" is released on video and hits No. 1 on Billboard's video charts.
-Dragonball Z debuts on TV, with violent scenes edited out.
-Cartoon Network airs unedited "Dragonball Z" episodes as part of its Toonami programming block.
-The "Pokemon" TV series launches, riding the popularity of the game franchise.
-Still largely unknown in the U.S., Miyazaki improves his profile with Miramax's release of "Princess Mononoke." Toon's PG-13 rating and limited release leads to modest box office, but draws strong reviews and attention to its creator. In Japan, it becomes the highest-grossing film of all time.
-Disney releases "Spirited Away," with English-language dubbing personally overseen by Pixar's John Lasseter. The film wins the animated feature Oscar.
-On television, "Yu-Gi-Oh" and "Inuyasha" both launch.
-Cartoon Network adds "Naruto" to its Toonami lineup.
-Nickelodeon debuts Avatar: The Last Airbender, a toon modeled after the style and content of Asian animation (mixing martial arts, mysticism and serial storytelling). Two years later, the show wins a primetime Emmy.
-Viz Media dubs manga-based toon "Bleach" for American auds. The show courts older viewers as part of Cartoon Network's Adult Swim block.
-Michael Bay directs a live-action version of Transformers hiring Peter Cullen to reprise his role as Optimus Prime.
-Paramount announces plans for an "Avatar" feature to be directed by M. Night Shyamalan.
The Wachowski brothers adapt Speed Racer as a live-action film.