The star formation histories (SFHs) of galaxies can tell us a great deal about the formation and evolution of galactic systems. By creating color-magnitude diagrams (CMDs) of resolved stellar populations, we can derive the star formation rate (SFR) as a function of time and metallicity (i.e., the SFH) for the observed stellar population. In this thesis, I study the methods used to make these measurements and calculations, and apply them to conduct a study of the Magellanic Clouds. Throughout this study, we aim to address two fundamental questions: “How can we obtain deep, spatially comprehensive photometric coverage of dwarf galaxies and use those data to construct accurate and meaningful SFHs?” and “Can we constrain the possible evolutionary scenarios of the Magellanic Clouds from their ancient SFHs?”We present the results from a study of the ancient star formation histories (SFHs) of the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC). At about 50 kpc and 60 kpc away, respectively, from the Milky Way (MW), the LMC and SMC provide us an excellent opportunity to make deep photometric measurement, allowing us to construct an accurate ancient SFH. Using archival data from the Hubble Space Telescope/Wide Field Planetary Camera 2 (HST /WFPC2), we construct CMDs for 56 LMC fields and 15 SMC fields. This data set provides diverse spatial coverage as well as photometric depth that reaches well below the oldest main sequence turn off (MSTO), allowing us to construct a global SFH of each galaxy with excellent temporal resolution, even in the oldest time bins. We derive the SFHs using the same maximum likelihood CMD fitting technique for both the LMC and the SMC to allow for the direct comparison of the results, without the introduction of unnecessary systematic offsets and uncertainties. At very early times, we find that the LMC experienced an initial burst of star formation activity that was absent in the SMC. After about 12 Gyr ago, the SFHs both galaxies tracked each other very well. After about 12 Gyr ago, they were both relatively quiescent until 4–6 Gyr ago, when the star formation rate (SFR) dramatically increased in both galaxies, and maintained that rate until the present. These findings have driven us to conclude that the MCs did not originally form together, and they are likely on their first passage through the MW. Finally, we discuss ongoing and upcoming studies of dwarf galaxies in the Andromeda system. Using ground-based and space-based data, we hope to derive spatially comprehensive SFHs with excellent temporal resolution. Accurate, quantitative SFHs of many of the Andromeda dwarfs will allow us to study a more significant portion of a whole galactic system than ever before. It will also have significant cosmological implications because we will be able to determine if the MW population is representative of galaxies in general or if the local environment plays a significant role in the evolution of a large galaxy.