A systematic approach is proposed to construct networks that can be controlled by destination tags. The networks can be designed so that they have a unique path between any of its inputs and any of its outputs and can also be designed so that multiple paths are provided. When multiple paths exist, the network is fault-tolerant in the sense that a fault in the path does not prevent communication through a redundant path. This approach is based on the fact that, for a unique-path network of size N with logN stages and 2x2 switches, a binary tree structure can be associated with each input switch. The tree is such that the root, nodes, edges and levels of the tree correspond to the input switch, switches connected to the input switch, links between these switches and stages of the network, respectively. Sets of tree structures can be devised and used as the underlying "skeletons" of fault-tolerant networks that are controllable by destination tags. There are several ways to organize binary trees and map them into networks in order to implement destination tag routing. This paper concentrates on a special case of the approach and experiments are conducted on constructing networks whose switches are 2x2, 3x3 or 4x4 switches (although nonuniform switches of various sizes are also possible.) Merits and advantages of these designs are discussed with respect to routing and rerouting schemes and fault tolerance. Several existing seemingly varied and independent designs of unique-path and fault-tolerant networks are found to be governed by this approach. In particular, Augmented Data Manipulator (ADM) networks and related designs are investigated and improved with respect to fault-tolerance and routing and rerouting schemes, and new designs with better fault-tolerance capabilities are suggested.