Optimization has become an essential modeling language and design method for communication networks. It has been widely applied to many key problems, including power control, coding, scheduling, routing, congestion control, content distribution, and pricing. It has also provided a fresh angle to view the interactions across a network protocol stack as the solutions to an underlying optimization problem. A unique requirement for optimization in networks is that the solution algorithm must be distributed. This has in turn motivated the development of new tools in distributed optimization. Many of these results have been well documented. In this chapter, we turn to a sample of three recent results on some of the challenging new issues, centered around the need to tackle combinatorial or robust optimization formulation through distributed algorithms. Much more on existing results, including proofs and numerical examples, can be found from the papers referenced here.