Many nonconvex optimization problems can be written as conic programs over a linear section of the semi-definite matrix cone with an additional rank 1 constraint. By dropping this rank 1 constraint, one obtains a semi-definite relaxation of the original problem. If the linear section is such that every extreme ray is a rank 1 matrix, then the relaxation will be exact. We shall call such spectrahedral cones "rank 1 generated". We describe the basic properties of rank 1 generated spectrahedral cones and provide some ways to construct such cones.