Many engineering applications are naturally modeled by systems of coupled nonlinear differential and algebraic equations (DAEs) that cannot be directly reduced to ODEs. Such systems (also referred to as ``high-index'' DAEs, singular systems, descriptor systems etc.) behave fundamentally different from ODEs (they do not have a smooth solution for arbitrary initial conditions, the solution may depend on derivatives of the forcing input etc.) and have been studied extensively from the point of view of numerical simulation. In this talk, recent results on the feedback control of nonlinear high-index DAEs will be presented. These rely on an algorithm for the derivation of state space realizations of the original DAE system or an equivalent feedback-modifed system. Connections with singular perturbations and chemical process applications will also be discussed.