Important milestones in the early history of General Relativity were the Einstein field equations, Schwarzschild's solution to them and the observational consequences of this solution. The Schwarzschild solution describes the space-time in the vicinity of a static, spherically symmetric mass, like the Sun, and the observational tests of this solution include the precession of the perihelion of planetary orbits – in particular the orbit of Mercury – and the bending of light in a gravitational field. A more recent test is the so-called radar echo delay of a signal sent from one planet (Earth) and reflected back from another one. An additional test of General Relativity, which depends only on the Equivalence Principle and not on the field equations, is the gravitational red-shift of light. The successful passing of these tests established General Relativity as the ‘correct’ theory of gravity. A feature of the Schwarzschild solution, not emphasised in the early days but given great prominence since, is the presence of the ‘Schwarzschild’ radius, which is the signature for the phenomenon of black holes. These matters are the concerns of this chapter. We begin with a comparison of the geodesic equation and the Newtonian limit of a weak, static gravitational field.