This report summarizes the state of the art in the application of medical tomography (CT) to petroleum recovery problems. A brief review of the basic principles of x-ray computerized tomography is followed by a discussion of the governing equations of the method. Calculation techniques and appropriate correlations for continued testing are described and discussed. A review of existing medical software is done. Consideration of the specific software needed for petroleum engineering as well as applications of new technologies such as image processing and computer networking are described. Criteria for the choice of a machine suitable for most petroleum-related applications are given. Emphasis is placed on flexibility, reliability, accuracy and price of the scanner. Two separate sections discuss positioning of the core and design of the core holders. Examples of possible applications of CT scanning to problems of geology, core analysis, EOR as well as operational process problems are discussed. 9 refs., 8 figs., 1 tab.