What is chaos? The contemporary idea of chaos in deterministic dynamical systems has its roots in the fundamental work of H. Poincare´ (1892), and is related to the real possibility of predicting the future of a given system. While a lot of fundamental research has been done to explain the full implications of chaotic behavior, the signature of chaos has been found with the help of modern numerical integrations in many systems of the real world, and specifically of astronomy, such as the orbits of our (and others) planetary systems, of many asteroids, in the rotation of planets and satellites.