We propose a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest path problem in an auxiliary network. We design tools and techniques for exploiting the network model in order to accelerate the identification of the frontier. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on four problem classes containing both linear and nonlinear objective functions.