The second phase of the Apache Point Observatory Galactic Evolution Experiment (APOGEE-2), a part of the Sloan Digital Sky Survey IV (SDSS-IV), will commence operations in 2014. APOGEE-2 represents a significant expansion over APOGEE-1, not only in the size of the stellar sample, but also in the coverage of the sky through observations in both the Northern and Southern Hemispheres. Observations on the 2.5m Sloan Foundation Telescope of the Apache Point Observatory (APOGEE-2N) will continue immediately after the conclusion of APOGEE-1, to be followed by observations with the 2.5m du Pont Telescope of the Las Campanas Observatory (APOGEE-2S) within three years. Over the six-year lifetime of the project, high resolution (R∼22,500), high signal-to-noise (≥100) spectroscopic data in the H-band wavelength regime (1.51-1.69 μm) will be obtained for several hundred thousand stars, more than tripling the total APOGEE-1 sample. Accurate radial velocities and detailed chemical compositions will be generated for target stars in the main Galactic components (bulge, disk, and halo), open/globular clusters, and satellite dwarf galaxies. The spectroscopic follow-up program of Kepler targets with the APOGEE-2N instrument will be continued and expanded. APOGEE-2 will significantly extend and enhance the APOGEE-1 legacy of scientific contributions to understanding the origin and evolution of the elements, the assembly and formation history of galaxies like the Milky Way, and fundamental stellar astrophysics.