In this paper we discuss heuristics for network air cargo revenue management. We start from a dynamic programming formulation of air cargo network revenue management. Since the curse of dimensionality makes this problem intractable, we suggest several methods, based on linear programming, approximate dynamic programming, and decomposition to obtain both upper bounds and heuristics. We prove relationships between the upper bounds. Furthermore, we analyze the performance of both the bounds as well as the heuristics in a numerical study. In this numerical study, we find that a dynamic programming decomposition yields the tightest bounds. The heuristic based on the decomposition dominates other approaches by giving higher expected net revenues both when applied on the single-leg and on the network cargo problem.