The Nuclear Spectroscopic Telescope Array (NuSTAR) launched in June 2012. With unprecedented sensitivity and angular resolution (57” HPD) in the 3-‐79 keV energy band, NuSTAR has opened a new window on the high-‐energy universe. One of its key targets is the Galactic center (GC) supermassive black hole Sagittarius A* (Sgr A*). Sgr A* is a remarkably underluminous supermassive black hole. Its current X-‐ray quiescence with luminosity of 10 33 erg s -‐1 is punctuated by flares up to a few times 10 35 erg s -‐1 . The flare production mechanism has remained unknown since its discovery. NuSTAR has detected six Sgr A* flares above 10 keV since 2012. It is the first time hard X-‐rays have ever been detected from Sgr A* flares. The spectra up to ~40 keV allow to distinguish between the emission mechanisms and point to the flare production processes. However, even during the most significant flares, the bolometric luminosity of Sgr A* is still orders of magnitudes lower than its Eddington luminosity. Whether it has ever experienced increased activity as observed in low-‐luminosity active galactic nuclei (AGN) is important in addressing the Sgr A* accretion mechanism. Indication of such a past activity of Sgr A* has come from observations of giant molecular clouds in the GC region. The NuSTAR observations of the GC molecular cloud Sgr B2 strongly support that its X-‐ray emission is due to reflection of a past giant outburst from Sgr A* with luminosity as high as 10 39 erg s -‐1 more than 100 years ago. Studies on other GC molecular clouds can further constrain the Sgr A* outburst history.