Nature has filled the upper right quadrant of the Hertzsprung-Russell diagram with more varieties of peculiar stars and odd chemical compositions than even our most speculative observers and theorists could dream up. To bring some structure to this vast subject I will categorize the phenomena we observe according to our model of stellar evolution, dividing the stars among the first ascent of the giant branch and the core-helium burning phase, the asymptotic giant branch (double shell-burning) phase, and the post-AGB and pre-planetary nebula stars. The types of stars found in these three groups are summarized below.