SPHEREx, a mission in NASA's Medium Explorer (MIDEX) program recently selected for Phase-A implementation, is an all-sky survey satellite that will produce a near-infrared spectrum for every 6 arcsecond pixel on the sky. SPHEREx has a simple, high-heritage design with large optical throughput to maximize spectral mapping speed. While the legacy data products will provide a rich archive of spectra for the entire astronomical community to mine, the instrument is optimized for three specific scientific goals: to probe inflation through the imprint primordial non-Gaussianity left on today's large-scale cosmological structure; to survey the Galactic plane for water and other biogenic ices through absorption line studies; and to constrain the history of galaxy formation through power spectra of background fluctuations as measured in deep regions near the ecliptic poles. The aluminum telescope consists of a heavily baffled, wide-field off-axis reflective triplet design. The focal plane is imaged simultaneously by two mosaics of H2RG detector arrays separated by a dichroic beamsplitter. SPHEREx assembles spectra through the use of mass and volume efficient linear variable filters (LVFs) included in the focal plane assemblies, eliminating the need for any dispersive or moving elements. Instead, spectra are constructed through a series of small steps in the spacecraft attitude across the sky, modulating the location of an object within the FOV and varying the observation wavelength in each exposure. The spectra will cover the wavelength range between 0.75 and 5.0 μm at spectral resolutions ranging between R=35 and R=130. The entire telescope is cooled passively by a series of three V-groove radiators below 80K. An additional stage of radiative cooling is included to reduce the long wavelength focal plane temperature below 60K, controlling the dark current. As a whole, SPHEREx requires no new technologies and carries large technical and resource margins on every aspect of the design.