Star formation in the central 0.5 pc of the Milky Way

The supermassive black hole candidate at the Galactic Center is surrounded by a parsec-scale star cluster, which contains a number of early type stars. The presence of such stars has been called a "paradox of youth" as star formation in the immediate vicinity of a supermassive black hole seemed difficult, as well as the transport of stars from far out in a massive-star lifetime. I will recall 30 years of technological developments which led to the current understanding of the nuclear cluster stellar population. The number of early type stars known at present is sufficient to access the 3D structure of this population and its dynamics, which in turn allows discriminating between the various possible origins proposed along the years.Comment: 8 pages, invited review for the conference "The Universe under the Microscope" (AHAR 2008), to be published in Journal of Physics: Conference Series by Institute of Physics Publishin