  Over the duration of the Kepler mission, KIC8462852 was observed to undergo
irregularly shaped, aperiodic dips in flux of up to $\sim 20$\%. The dipping
activity can last for between 5 and 80 days. We characterize the object with
high-resolution spectroscopy, spectral energy distribution fitting, radial
velocity measurements, high-resolution imaging, and Fourier analyses of the
Kepler light curve. We determine that KIC8462852 is a typical main-sequence F3
V star that exhibits no significant IR excess, and has no very close
interacting companions. In this paper, we describe various scenarios to explain
the dipping events observed in the Kepler light curve. We confirm that the
dipping signals in the data are not caused by any instrumental or data
processing artifact, and thus are astrophysical in origin. We construct
scenario-independent constraints on the size and location of a body in the
system that is needed to reproduce the observations. We deliberate over several
assorted stellar and circumstellar astrophysical scenarios, most of which have
problems explaining the data in hand. By considering the observational
constraints on dust clumps in orbit around a normal main-sequence star, we
conclude that the scenario most consistent with the data in hand is the passage
of a family of exocomet or planetesimal fragments, all of which are associated
with a single previous break-up event, possibly caused by tidal disruption or
thermal processing. The minimum total mass associated with these fragments
likely exceeds $10^{-6}$~\mearth, corresponding to an original rocky body of
$>100$~km in diameter. We discuss the necessity of future observations to help
interpret the system.
