Inverting Phase Curves to Map Exoplanets

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.