Appears in collection : Colloque Scientifique International Poincaré 100

One of Poincaré's most important contributions to dynamical systems theory was his discovery of chaotic behavior in the three-body problem. Specifically, he famously described but refused to draw the complicated tangle of stable and unstable manifolds which occurs when transverse homoclinic orbits exist. In the century since his death, other kinds of chaotic motions of the three-body problem have been found. I will show some of the ways chaos can arise in celestial mechanics. With the help of the computer, I will present some pictures that Poincaré surely would have appreciated.