Detailed chemical abundances of globular clusters in the Milky Way and M31 (the Andromeda Galaxy) are presented based on analyses of high resolution spectra. The unusual Milky Way cluster Palomar 1 (Pal 1) is studied through spectra of individual red giant branch stars; these abundances show that Pal 1 is not a classical globular cluster, and may have been accreted from a dwarf satellite of the Milky Way. The Milky Way globular clusters 47 Tuc, M3, M13, NGC 7006, and M15 are studied through their integrated light (i.e. a single spectrum is obtained for each cluster) in order to test high resolution integrated light analyses. The integrated abundances from these clusters reproduce the average abundances from individual stellar analyses for elements that do not vary within a cluster (e.g. Fe, Ca, and Ni). For elements that do vary within the clusters (e.g. Na and Mg) the integrated abundances fall within the observed ranges from individual stars. Certain abundance ratios are found to be extremely sensitive to uncertainties in the underlying stellar populations, such as input models, empirical relations to determine atmospheric parameters, interloping field stars, etc., while others (such as [Ca I/Fe I]) are largely insensitive to these effects. With these constraints on the accuracy and precision of high resolution integrated light analyses, detailed abundances are obtained for seven clusters in the outer halo of M31 that were recently discovered in the Pan-Andromeda Archaeological Survey (PAndAS) and are likely to have originated in dwarf galaxy satellites. Three clusters are relatively metal rich ([Fe/H] > −1.5) for their locations in the outer halo; their chemical abundances suggest that they likely originated in one or more fairly massive dwarf satellities. The other four are more metal-poor, and may have originated in less massive dwarf satellites. These results indicate that the Milky Way and M31 have both experienced some amount of accretion from dwarf satellites, though M31 may have had a more active accretion history. / Graduate