In textbook descriptions of Newton's cradle, it is generally claimed that displacing one ball will result in a collision that leads to another ball being ejected from the line, with all others remaining motionless. Hermann and Schmälzle, Hinch and Saint-Jean, and others have shown that a realistic description is more subtle. We present a simulation of Newton's cradle that reproduces the break-up of the line of balls at the first collision, the eventual movement of all the balls in phase, and is in good agreement with our experimentally obtained data. The first effect is due to the finite elastic response of the balls, and the second is a result of viscoelastic dissipation in the impacts. We also analyze a dissipation-free ideal Newton's cradle which displays complex dynamics.