In the recent years, the Cryogenic Circuit Conductor and Coil (4C) code has been developed to allow the thermal-hydraulic modeling of superconducting magnets and their cryogenic circuit in the frame of nuclear fusion devices. The code consists of different modules, describing the SC winding, the structures, their cooling paths and the external SHe cryogenic circuit, respectively. 4C was successfully applied to model different kinds of transients on different magnet systems, with time scales spanning from week-long cool-down to very fast current dump, and with space scales ranging from the whole magnet to a portion of a single conductor. In this paper the main aspects of the 4C are presented, with particular emphasis on its capability to capture the main features of the magnet systems of International Thermonuclear Experimental Reactor (ITER