In process vessels, involving two or three phases it is often important not only to know the volume fraction (holdup) of each phase but also the spatial distribution of such holdups. This information is needed in control, trouble shooting and assessment of flow patterns and can be observed noninvasively by the application of Computed Tomography (CT). This report presents a complete overview of X-ray and gamma ray transmission tomography principles, equipment design to specific tasks and application in process industry. The fundamental principles of tomography, the algorithms for image reconstruction, the measurement method and the possible sources of error are discussed in detail. A case study highlights the methodology involved in designing a scanning system for the study of a given process unit, e.g., reactor, separations column etc. Results obtained in the authors` laboratory for the gas holdup distribution in bubble columns are also presented. Recommendations are made for the Advanced Fuels Development Unit (AFDU) in LaPorte, TX.