This susrvey is on modelling of various network design problems with tree configuration, which have a wide variety of practical applications, particularly in communication, which have a wide a variety of practical applications, particularly in communication and transportation network planning. Models which can be classified as either minimum spanning tree of Steiner tree, are investigated. Various important variants of each basic model are then classified according to model structurs. In addition to the calssification, the typical solution method for each problem is briefly sketched, along with some remarks on further research issues.