This report is a sequel to our review paper, Lemoine [Lemoine, A. J. 1977. Networks of queues-A survey of equilibrium analysis. Management sci. 24 464-481.], on the equilibrium analysis of networks of queues. In this paper we review some weak convergence results for networks of queues, which include heavy traffic limit theorems for open networks and asymptotic results for large closed Markovian systems which are generalizations of the classical repairman problem. These weak convergence results justify certain approximation schemes for processes of interest. We also discuss some important open problems in the area of weak convergence results for networks of queues.