Quantitative X-ray CT imaging is needed in a number of medical imaging applications. It has been proposed for precisely determining the position and orientation of radiation brachytherapy applicators in the treatment of cervical cancer. It is needed for imaging in the presence of high density objects such as dental implants, cochlear implants, and orthopedic implants. Our approach to these problems is based on a detailed physical model for the data. The model incorporates as many physical properties as possible, including Beer's law, the energy spectrum of the x-ray source, the point spread function, and the counting statistics of the detectors. The image or volume reconstruction problem is formulated as a maximum likelihood estimation problem. A family of iterative algorithms is derived for different variations of the problem. Some of the properties of the algorithm and implementations on phantom data are presented. Joint work with D. L. Snyder, B. Whiting, J. Williamson, J. Benac, R. Murphy, D. Politte, and S. Yan.