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There are seven official concerts that took place, not counting similarities of set lists. In addition to the official concerts, several unofficial concerts have been performed (including some illegal ones). Refer to Vocaloid Concert Song List on vocaloid.wikia.com for more details and an in-depth set list for all the concerts.
Miku's first live appearance was during Animelo, where Miku only appeared for a brief moment dancing and singing "Miku Miku ni Shite Ageru". Afterward, the band played "BLACK★ROCK SHOOTER" while the PV for the song was displayed on the screen. It was not a true concert, but it is one of Miku's first live appearances.
Her second live appearance was during MikuFES '09, where Miku performed songs with popular guest producers on a transparent glass screen in Shinkiba Tokyo. Unlike the following concerts, this concert featured only Hatsune Miku. This performance was more of a showcase for the producers than an actual "concert", but it influenced the idea of having guest producers on stage for the following concerts.
The first true concert, and the third official live appearance by Hatsune Miku, was performed in 2010 and called Miku no Hi Kanshasai 39's Giving Day. SEGA and Crypton Future Media were promoting this event as part of the rhythm game published by SEGA entitled "Hatsune Miku Project DIVA". As part of the promotion, the models used in the concert were SEGA Project DIVA Dreamy Theater models, with the exception of two songs in the middle of the concert where they switched to the original Project DIVA model.
The next live appearance was an unofficial concert (not sponsored by SEGA or Crypton) on NicoNicoDouga Daikaigi 2011 Japan Tour. The models used to create the mini-concert were MikuMikuDance (MMD) models. It was the first MMD mini-concert, and was performed by Miku and Rin.
The second true concert (and the fourth official live appearance) featured the four Character Vocaloid (Hatsune Miku, Kagamine Rin, Kagamine Len, and Megurine Luka). It was named Hatsune Miku's Live Party: 39s Live in Tokyo and, like the previous year's concert, was held on March 9. Unlike the previous year's concert, this featured models by Marza Animation Planet and was produced by 5pb. This particular concert was broadcasted in several theaters throughout Japan. However, it did not use the transparent glass screen to present the singers; it used a more traditional opaque black screen.
The third true concert is Mikunopolis, a concert that took place outside of Japan in Los Angeles. It was Miku's first official overseas concert, and had slightly upgraded SEGA Project DIVA models from the 2010 concert.
The fourth true concert took place in Sapporo, Hokkaido, entitled Hatsune Miku's Live Party 39s Live in Sapporo. It was essentially the same as the one that took place during March 9, 2011, with a few notable changes to the set list. It also brought back the glass screen, keeping the opaque screen mounted above the stage for certain songs. There was no NicoNicoDouga live broadcast, but they broadcasted the concert to two more additonal theaters outside of Japan, in Taiwan and Hongkong.
A small concert took place in Mexico City's TNT with Miku and other "Fanmade Vocaloids" performing. It was not sponsored by Crypton or Sega in anyway, but had MMD models and other characters such as Touhou and UTAUloids. This concert is widely regarded as illegal, due to the fact that TnT performed the concert for commercial purposes. They did not apply for permission to use the VOCALOID engine to create custom characters, nor did they request permission to use the UTAU Kasane Teto in a commercial environment. They also did not contact song producers for their consent. All of these legalities are required to perform a legal fanmade concert.
A fanmade concert took place in Takarazuka University in Japan on Sept 18 to 19. It featured college students making a mini concert from scratch.
The fifth official concert, a sequel to the Mikupa Sapporo Concert, has taken place in Singapore as part of the Anime Festival Asia I LOVE ANISONG event. It modified the Sapporo concert set list slightly to introduce a few new songs.
During the sixth and seventh official concerts, the Mikupa Singapore (2011) and Mikunopolis in Los Angeles (2011) concert sets were slightly modified in 2012 for the March 8 (Mikupa) and March 9 (Miku no Hi Dai-Kanshasai) Many 39s Giving Day concerts.