Adopting centralized optimization approaches in order to solve optimization problem arising from analyzing large-scale systems, requires a powerful computational unit. Such units, however, do not always exist. In addition, it is not always possible to form the optimization problem in a centralized manner due to structural constraints or privacy requirements. A possible solution in these cases is to use distributed optimization approaches. Many large-scale systems have inherent structures which can be exploited to develop scalable optimization approaches. In this thesis, chordal graph properties are used in order to design tailored distributed optimization approaches for applications in control and estimation, and especially for model predictive control and localization problems. The first contribution concerns a distributed primal-dual interior-point algorithm for which it is investigated how parallelism can be exploited. In particular, it is shown how the computations of the algorithm can be distributed on different processors so that they can be run in parallel. As a result, the algorithm execution time is accelerated compared to the case where the algorithm is run on a single processor. Simulation studies on linear model predictive control and robust model predictive control confirm the efficiency of the framework. The second contribution is to devise a tailored distributed algorithm for nonlinear least squares with application to a sensor network location problem. It relies on the Levenberg-Marquardt algorithm, in which the computations are distributed using message passing over the computational graph of the problem, which is obtained from what is known as the clique tree of the problem. The results indicate that the algorithm provides not only a good localization accuracy, but also it requires fewer iterations and communications between computational agents in order to converge compared to known first-order methods. The third contribution is a study of extending the message passing idea in order to design tailored distributed algorithm for general non-convex problems. The framework relies on an augmented Lagrangian algorithm in which a primal-dual interior-point method is used for the inner iteration. Application of the framework for general model predictive control of systems with several interconnected sub-systems is extensively investigated. The performance of the framework is then compared with distributed methods based on the alternating direction method of multipliers, where the superiority of the framework is illustrated.