  These lecture notes are based on lectures given by the author at the summer
school "Arrangements in Pyr\'en\'ees" in June 2012. We survey and compare
various compactifications of complex hyperplane arrangement complements. In
particular, we review the Gel'fand-MacPherson construction, Kapranov's visible
contours compactification, and De Concini and Procesi's wonderful
compactification. We explain how these constructions are unified by some ideas
from the modern origins of tropical geometry. The paper contains a few new
arguments intended to make the presentation as self-contained as possible.
