The following report reviews the development and state of engineering economic applications of the second law of thermodynamics. It encompasses virtually all of the work carried out publicly in the United States, and to the best of our knowledge that done in other countries (but also see Tsatsaronis, 1987). The ultimate objective here is to provide direction for future research on the fundamentals and applications of this subject, and for the support thereof. We begin with a historical review, which is important for better comprehension of second law costing, its objectives, its state, and its prospects. Following the history, further relevant background, on cost accounting, is presented in Part II. Part III describes in general terms the different exergy costing methods which are in existence. Parts IV and V constitute the nucleus of the report. Therein the various techniques are analyzed and critiqued, generally by considering successive publications developing and/or based on a technique. Part IV is devoted to algebraic methods for determining and applying exergy costs and Part V, to be presented in the sequel to this article, to calculus methods. These two parts do refer to each other, and the relationships between them are developed. Suggestions regarding further research are incorporated into both sections. It should be mentioned that the references we cite are not intended to be exhaustive. However, it is our intention to refer to the most recent work of each author, so that the reader may trace back to earlier publications. Also, the bibliographies of Wepfer (1979) and Liu and Wepfer (1983) are quite exhaustive.