Dwarf spheroidal galaxies (dSphs) are the smallest, most numerous, and among the oldest galaxies in the Universe. Since their discovery in the 1930;;s, dSphs have provided insights into ancient stellar populations, galaxy formation, and early Universe star formation. Beginning in the 1980;;s, spectroscopy revealed anomalous stellar kinematics within dSph galaxies, which is typically interpreted as considerable amounts of dark matter (DM) existing in these systems. One kinematic effect that could mimic DM arises from the orbital motions of binary stars; however, subsequent work found that binaries alone could not account for the anomalous kinematics within the larger dSph galaxies. The recent discovery of a new class of dSphs called ;;ultra-faints;; has reignited the issues of binaries due to the intrinsically low velocity dispersions in these systems. Motivated by the need to better understand the extent of binary contamination in ultra-faints, this dissertation draws upon both recent and archival data in brighter dSphs to determine updated kinematic properties and to provide a fresh look at the binary fraction within dSphs. The spectroscopic data used in this dissertation comes from many different telescopes and instruments, spans 2-3 decades in time, and concerns three dSphs: Leo II, Draco, and Ursa Minor. For Leo II, our analysis included a new study of the galaxy;;s internal kinematics, finding among other results, (a) the V-band mass-to-light ratio is 15.2+-5.5, (b) no signs of internal rotation, and (c) suggestive evidence of kinematic substructure related to metallicity. The full kinematic datasets for all three dwarfs were used to characterize the likely binary fraction of each galaxy under the assumption that velocity fluctuations for individual stars with multiple observations were due to binaries. The process we followed was to first generate Monte Carlo simulations of the observations, whereby binary fraction was varied. Then we performed a Bayesian analysis that compared the simulations with the data to discern the most likely binary fraction in each dSph. We explored various mass ratio, eccentricity, and period distributions throughout the simulations. We also applied our method to preexisting data in Carina, Fornax, Sculptor, and Sextans to yield a homogeneous measurement of binary fraction in seven dwarfs -- the largest sample to date. The probability that the binary fraction is the same (i.e., exists within a range of fractions spanning 20%) amongst these dwarfs is <1%. We generally found no significant correlations between binary fraction and other galactic properties, though we cannot rule out a weak dependence with star-formation history.Given the variability of binary fraction that we inferred between galaxies, we modeled the effects of binaries on the global kinematics of mock dwarf galaxies as a function of binary fraction. We simulated different intrinsic dispersions for dwarfs, sample sizes, number of observations, and size of velocity errors. Unless the binary fraction is low (<10%), binaries will have a non-negligible effect on the observed velocity dispersion of ultra-faints. Recent observations do show cases where binaries have a significant effect. We illustrate that this can be partially mitigated by numerous observations, removing obvious velocity variables, and averaging the remaining stars in the velocity dispersion calculation. The results of this work illustrate that multi-epoch radial velocity measurements of additional stars will be necessary to better understand binary fractions, binary parameter distributions, and the role binaries have in distorting the inferred global kinematics of the smallest galaxies.
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