  One of the most exciting results of the Spitzer era has been the ability to
construct longitudinal brightness maps from the infrared phase variations of
hot Jupiters. We presented the first such map in Knutson et al. (2007),
described the mapping theory and some important consequences in Cowan & Agol
(2008) and presented the first multi waveband map in Knutson et al. (2008). In
these proceedings, we begin by putting these maps in historical context, then
briefly describe the mapping formalism. We then summarize the differences
between the complementary N-Slice and Sinusoidal models and end with some of
the more important and surprising lessons to be learned from a careful analytic
study of the mapping problem.
