  Since the discovery of the first exoplanets more than 20 years ago, there has
been an increasing need for photometric and spectroscopic models to
characterize these systems. While imaging has been used extensively for Solar
System bodies and extended objects like galaxies, the small angular extent of
typical planetary systems makes it difficult or impossible to resolve them.
Spatially integrated observations like measuring the total brightness or
spectrum, however, can be conducted at a resonable cost. This thesis focuses on
photometric models in the context of transiting systems, which exhibit a number
of phenomena that can be exploited for characterization.
  First, we showcase the popular methods of transiting exoplanet discovery and
characterization by ground based observations on the hot Jupiter HAT-P-27b. We
demonstrate how transits allow us to constrain planetary mass, radius, and
orbital inclination, which would not be possible based only on, for example,
radial velocity measurements.
  Next, we perform reflection spectroscopy on HAT-P-1b, another hot Jupiter,
using the binary companion of the host star as a reference to remove systematic
errors from the signal. Here the transiting nature of the system allows us to
look for the very faint light reflected by the planet.
  We also apply the idea of planetary transits to investigate the feasibility
of transit observations in astrophysical systems of very different scale: stars
in galactic nuclei potentially transiting the accretion disk of the
supermassive black hole in the galactic center.
  Finally, we focus on mapping spots on the stellar surface using transits.
This method has been used for a decade, and helped constrain stellar rotation
or orbital geometry in a number systems. We study starspots on HAT-P-11 to
learn more about stellar rotation and to investigate the size and contrast of
the spots themselves.
