Stochastic models of complex networks with limited resources arise in a wide variety of applications in science and engineering, e.g., in manufacturing, transportation, telecommunications, computer systems, customer service facilities, and systems biology. Bottlenecks in such networks cause congestion, leading to queueing and delay. Sharing of resources can lead to entrainment effects. Understanding the dynamic behavior of such modern stochastic networks present challenging mathematical problems. \\ \\ This talk will describe some developments in this area. A key feature will be dimension reduction, resulting from entrainment due to resource sharing. An example of bandwidth sharing in a data network will be featured.