Recursive transition networks (RTNs) are used to define languages by representing them as graphs with nodes and labeled edges. Strings in the language are produced by paths from a start node to a final node, where the labels of the edges along the path combine to form the string. RTNs allow for defining infinite languages more efficiently than listing all strings, as adding edges increases the number of possible paths and strings. The power of RTNs increases dramatically when cycles are added to the graph, allowing for infinitely many possible paths and strings.