The authors report the discovery of 9,088 new spectroscopically confirmed white dwarfs and subdwarfs in the Sloan Digital Sky Survey (SDSS) Data Release 10 (DR10). They obtain T_eff, log g and masses for hydrogen-atmosphere white dwarf stars (DAs) and helium-atmosphere white dwarf stars (DBs), and estimate the calcium/helium abundances for the white dwarf stars with metallic lines (DZs) and carbon/helium for carbon-dominated spectra (DQs). They found 1 central star of a planetary nebula, 2 new oxygen spectra on helium-atmosphere white dwarfs, 71 DQs, 42 hot DO/PG1159s, 171 white dwarf+main-sequence star binaries, 206 magnetic DAHs, 327 continuum-dominated DCs, 397 metal-polluted white dwarfs, 450 helium-dominated white dwarfs, 647 subdwarfs and 6887 new hydrogen-dominated white dwarf stars. The targeted white dwarfs were required to be point sources with clean photometry, and to have USNO-B Catalog counterparts (Monet et al.. 2003, AJ, 125, 984, CDS Cat. I/284). They were also restricted to regions inside the DR7 imaging footprint and required to have colors within the ranges g < 19.2, (u-r) < 0.4, -1 < (u-g) < 0.3, -1 < (g-r) < 0.5 and to have low Galactic extinction A_r < 0.5 mag. Additionally, targets that did not have (u-r) < -0.1 and (g-r) < -0.1 were required to have USNO proper motions larger than 2 arcseconds per century (20 milliarcseconds per year). Objects satisfying the selection criteria that had not been observed previously by the SDSS were denoted by the WHITEDWARF_NEW target flag, while those with prior SDSS spectra are assigned the WHITEDWARF_SDSS flag. Some of the latter were re-observed with BOSS in order to obtain the extended wavelength coverage that the BOSS spectrograph offers. The color selection used includes DA stars with temperatures above ~14,000 K, helium-atmosphere white dwarfs above ~8000 K, as well as many rarer classes of white dwarfs. Hot subdwarfs (sdB and sdO) were targeted as well. Note that this catalog does not include stars from the earlier SDSS white dwarf catalogs, e.g., Eisenstein et al. (2006, ApJS, 167, 40, available in the HEASARC database as the SDSSDWDSD table), Kleinman et al. (2013, ApJS, 205, 5, available in the HEASARC database as the SDSSDR7WD table).. This table was created by the HEASARC in October 2017 based on an electronic version of Table 6 from the reference paper which was obtained from the CDS as their catalog J/MNRAS/446/4078 file table6.dat. This is a service provided by NASA HEASARC .