The classical theory of total positivity concerns matrices in which all minors are nonnegative. While this theory was pioneered in the 1930's, the past decade has seen a flurry of research in this area initiated by Lusztig, who extended the theory to real reductive groups and real flag varieties. In this talk we will describe the combinatorics and topology of the totally nonnegative part of a real flag variety, and of its CW decomposition.