Robustness of optimization models for networking problems has been an under-explored area. Yet most existing algorithms for solving robust optimization problems are centralized, thus not suitable for many communication networking problems that demand distributed solutions. This paper represents the first step towards building a framework for designing distributed robust optimization algorithms. We first discuss several models for describing parameter uncertainty sets that can lead to decomposable problem structures. These models include general polyhedron, D-norm, and ellipsoid. We then apply these models to solve robust power control in wireless networks and robust rate control in wireline networks. In both applications, we propose distributed algorithms that converge to the optimal robust solution. Various tradeoffs among performance, robustness, and distributiveness are illustrated both analytically and through simulations.