The paper gives an overview of inertia-controlling quadratic programming (QP) methods. The authors present a uniform description of primal-feasible QP methods for nonconvex problems with a nonempty feasible region. The search directions are defined by equation systems which are based on the Karush-Kuhn-Tucker system and depend on the definiteness of the reduced Hessian of the quadratic objective function. Some rules are given for deleting constraints from and adding constraints to the working active set that defines the reduced Hessian. The possibility of factorization of the reduced Hessian is discussed briefly. In a theoretical background the connections to the Schur complement for analysing the iterates and to Sylvester's law of inertia are described.