  For much of human history we have wondered how our solar system formed, and
whether there are any other planets like ours around other stars. Only in the
last 20 years have we had direct evidence for the existence of exoplanets, with
the number of known exoplanets dramatically increasing in recent years,
especially with the success of the Kepler mission. Observations of these
systems are becoming increasingly more precise and numerous, thus allowing for
detailed studies of their masses, radii, densities, temperatures, and
atmospheric compositions. However, one cannot accurately study exoplanets
without examining their host stars in equal detail, and understanding what
assumptions must be made to calculate planetary parameters from the directly
derived observational parameters.
  In this thesis, I present observations and models of the primary transits and
secondary eclipses of transiting exoplanets from both the ground and Kepler in
order to better study their physical characteristics and search for additional
exoplanets. I then identify, observe, and model new eclipsing binaries to
better understand the stellar mass-radius relationship and stellar
limb-darkening, compare these observations to the predictions of stellar
models, and attempt to define to what extent these fundamental stellar
characteristics can impact derived planetary parameters. I also present novel
techniques for the direct determination of exoplanet masses and stellar
inclinations via multi-wavelength astrometry, the ground-based photometric
observation of stars at sub-millimagnitude precision, the reduction of Kepler
photometry from pixel-level data, the extraction of radial velocities from
spectroscopic observations, and the automatic identification, period analysis,
and modeling of eclipsing binaries and transiting planets in large datasets.
