The planets in the solar system have completed about a thousand million orbits since they were born. The behavior of planetary orbits over such long times is one of the oldest problems in physics, but was not understood until recently despite three centuries of study. Recent advances in computer hardware and algorithms now allow us to follow the motion of planets reliably for the lifetime of the solar system. These studies help to answer questions such as: How has the Earth’s orbit evolved throughout geological history, and what is the Earth’s ultimate fate? What determines the number and spacing of the planets? And what are the likely properties of other planetary systems?