We consider graphs created on a randomly scattered set of vertices in Euclidean d-space, by placing an edge between any two vertices at most unit distance apart. When the underlying set of vertices is an infinite homogeneous Poisson process, this graph is called the Gilbert graph; when it is a finite set of points in a cube, it is called the random geometric graph. We discuss basic notions notions for the Gilbert graph such as cluster size distribution, and phase transition for infinite components. We also relate these notions to asymptotic properties of the random geometric graph.