The central parsec of our Galaxy hosts not only a supermassive black hole, but also a large population of young stars (age <6 Myr) whose presence is puzzling given how inhospitable the region is for star formation. The strong tidal forces require gas densities many orders of magnitude higher than is found in typical molecular clouds. Kinematic observations of this young nuclear cluster show complex structures, including a well-defined inner disk, but also a substantial off-disk population. Spectroscopic and photometric measurements indicate the initial mass function (IMF) differs significantly from the canonical IMF found in the solar neighborhood. These observations have led to a number of proposed star formation scenarios, such as an infalling massive star cluster, a single infalling molecular cloud, or cloud-cloud collisions. I will review recent works on the young stars in the central parsec and discuss connections with young nuclear star clusters in other galaxies, such as M31, and with star formation in the larger central molecular zone.