Work and Heat Exchange Network (WHEN) design has been an emerging topic in the area of Process Synthesis and has attracted increasing research interest in the past few years. Not only temperature changes but also pressure changes of process streams have been taken into consideration in WHEN design. As a result, pressure changing equipment such as compressors, expanders, pumps, valves, etc., as well as traditional heat exchange equipment is included in WHEN design. Similar to HEN design problems, both graphical and mathematical optimization approaches have been under development for WHEN design. The graphical approaches utilize fundamental thermodynamic insight while mathematical optimization approaches enable dealing with large size problems. This paper focuses on a comparison between the graphical and mathematical optimization approaches for WHEN design. A case study is used to illustrate the importance of thermodynamic insight in WHEN design even in the case of using mathematical optimization approaches.