Dieter Kratsch Metz, France AT-free graphs: structure and algorithms Three mutually different vertices of a graph are said to be an asteroidal triple if between any two of them there is a path avoiding the neighborhood of the third. Graphs without asteroidal triple are called AT-free graphs. AT-free graphs contain various well-known classes of perfect graphs, as e.g., interval, permutation and trapezoid graphs. A lot of research on AT-free graphs has been done in the last 20 years. We present some fundamental structural properties of AT- free graphs and discuss the algorithmic complexity of some NP-hard problems on AT-free graphs.