The purpose of our work has been to develop a mathematical basis for the use of light in medical diagnosis and therapy. Studies have recently involved analyses of methods for the non-invasive diagnosis of tumors. Other studies relate to optical properties of deep lying tissue, for example to determine the oxygenation state of hemoglobin in the brain. Included among recent projects is a mathematical investigation of resolution limits for time-resolved imaging of human breast. In this project we derived an analytical theory to calculate the line spread function of time-resolved photons as they cross different planes inside a finite slab. Experimental confirmation of this theory has been obtained from experiments done with collaborators at University College, London. Another recent project is directed towards the development of an analytical theory to assess the contrast obtainable in a transillumation measurement. This study realistically accounts for the fact that the absorbance of a tissue inclusion may not be very different from that of normal tissue. We have derived a theory that presently pertains to relatively small localized targets. This work currently is being extended to targets of arbitrary size and shape. The ultimate goal is to develop an iterative scheme for inverting transmission data to reconstruct images from actual tissue.