The emergence of new technologies offers continual improvement in the diagnosis and treatment of cancer and other diseases. Intensity-modulated radiotherapy (IMRT) is a new form of three-dimensional conformal radiotherapy. IMRT is designed to address a major limitation of conventionally delivered radiotherapy: its inability to restrict the treatment beam to the tumor-bearing tissue. To produce IMRT treatment plans, optimization methods have been used for designing the beam fluence pattern. Since multiple beams are used, calculation of intensities across any one beam must consider the contribution of from all other beams. Determining the optimal intensity-modulation, therefore, is a difficult problem. It is sometimes referred to as the "inverse problem" for radiotherapy treatment planning. This talk will present background information on radiation therapy and IMRT as well as research and case results from optimization methods using mixed-integer programming applied to IMRT. A clinical procedure for an IMRT treatment will be presented. This research was produced through a joint collaboration with the Department of Radiation Oncology at Emory University and Georgia Tech's School of Industrial & Systems Engineering. The work presented is joined with Ian Crocker and Eva Lee.