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SPHEREx is a proposed SMEX mission selected for Phase A. SPHEREx will carryout the first all-sky spectral survey and provide for every 6.2" pixel aspectra between 0.75 and 4.18 $\mu$m [with R$\sim$41.4] and 4.18 and 5.00$\mu$m [with R$\sim$135]. The SPHEREx team has proposed three specific scienceinvestigations to be carried out with this unique data set: cosmic inflation,interstellar and circumstellar ices, and the extra-galactic background light.It is readily apparent, however, that many other questions in astrophysics andplanetary sciences could be addressed with the SPHEREx data. The SPHEREx teamconvened a community workshop in February 2016, with the intent of enlistingthe aid of a larger group of scientists in defining these questions. This papersummarizes the rich and varied menu of investigations that was laid out. Itincludes studies of the composition of main belt and Trojan/Greek asteroids;mapping the zodiacal light with unprecedented spatial and spectral resolution;identifying and studying very low-metallicity stars; improving stellarparameters in order to better characterize transiting exoplanets; studyingaliphatic and aromatic carbon-bearing molecules in the interstellar medium;mapping star formation rates in nearby galaxies; determining the redshift ofclusters of galaxies; identifying high redshift quasars over the full sky; andproviding a NIR spectrum for most eROSITA X-ray sources. All of theseinvestigations, and others not listed here, can be carried out with the nominalall-sky spectra to be produced by SPHEREx. In addition, the workshop definedenhanced data products and user tools which would facilitate some of thesescientific studies. Finally, the workshop noted the high degrees of synergybetween SPHEREx and a number of other current or forthcoming programs,including JWST, WFIRST, Euclid, GAIA, K2/Kepler, TESS, eROSITA and LSST.

Science Impacts of the SPHEREx All-Sky Optical to Near-Infrared Spectral  Survey: Report of a Community Workshop Examining Extragalactic, Galactic,  Stellar and Planetary Science