The Nuclear Spectroscopic Telescope Array (NuSTAR) mission, launched on 2012 June 13, is the first focusing high-energy X-ray telescope in orbit. NuSTAR operates in the band from 3 to 79 keV, extending the sensitivity of focusing far beyond the ~10 keV high-energy cutoff achieved by all previous X-ray satellites. The inherently low background associated with concentrating the X-ray light enables NuSTAR to probe the hard X-ray sky with a more than 100-fold improvement in sensitivity over the collimated or coded mask instruments that have operated in this bandpass. Using its unprecedented combination of sensitivity and spatial and spectral resolution, NuSTAR will pursue five primary scientific objectives: (1) probe obscured active galactic nucleus (AGN) activity out to the peak epoch of galaxy assembly in the universe (at z ≲ 2) by surveying selected regions of the sky; (2) study the population of hard X-ray-emitting compact objects in the Galaxy by mapping the central regions of the Milky Way; (3) study the non-thermal radiation in young supernova remnants, both the hard X-ray continuum and the emission from the radioactive element 44Ti; (4) observe blazars contemporaneously with ground-based radio, optical, and TeV telescopes, as well as with Fermi and Swift , to constrain the structure of AGN jets; and (5) observe line and continuum emission from core-collapse supernovae in the Local Group, and from nearby Type Ia events, to constrain explosion models. During its baseline two-year mission, NuSTAR will also undertake a broad program of targeted observations. The observatory consists of two co-aligned grazing-incidence X-ray telescopes pointed at celestial targets by a three-axis stabilized spacecraft. Deployed into a 600 km, near-circular, 6° inclination orbit, the observatory has now completed commissioning, and is performing consistent with pre-launch expectations. NuSTAR is now executing its primary science mission, and with an expected orbit lifetime of 10 yr, we anticipate proposing a guest investigator program, to begin in late 2014.