In this chapter we show that chordal structure can be used to devise efficient optimization methods for many common model predictive control problems. The chordal structure is used both for computing search directions efficiently as well as for distributing all the other computations in an interior-point method for solving the problem. The chordal structure can stem both from the sequential nature of the problem as well as from distributed formulations of the problem related to scenario trees or other formulations. The framework enables efficient parallel computations.