The question of whether globular clusters (GCs) host black holes (BHs) has been a long-standing question in astronomy. Because of the dynamics of the crowded globular cluster environment, they should be extremely efficient at forming black hole-black hole binaries (BBHs), such as those detected merging by LIGO. LIGO is detecting many more (and more massive!) BBHs than was ever expected, and a first step to understanding the formation of these binaries is to understand BHs in GCs. However, very few ways exist to study BHs in GCs observationally, and there is only one effective method to study BH candidates in extragalactic GCs: by studying ultraluminous X-ray sources (ULXs) that are associated with GCs. Because their X-ray luminosities far exceed the Eddington limit for a stellar mass BH, ULXs in GCs are good BH candidates. However, they are very rare, with only a few per galaxy (with only 10 currently known sources among 3 galaxies). In this thesis, we study a total of 9 ULX sources that are associated with globular clusters in both X-ray and optical. One of these, RZ2109, shows extreme variability across more than 15 years of monitoring in X-ray, with changes of almost an order of magnitude on the order of days. Typically any variability in flux is expected to be correlated with a change in the spectral properties of the source (i.e. some physical change in the system), however, the shape of the X-ray spectrum of RZ2109 remains the same across all observations. X-ray and optical studies of all 9 GC ULXs indicate a potential correlation between the X-ray spectrum and presence of optical emission beyond the cluster continuum--one of the few X-ray-optical correlations known for astronomical objects. Lastly, we present long-term monitoring in optical of RZ2109 shows a broad [OIII] emission line which declines long-term over almost ten years, and then re-brightens.
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