  This is the manuscript of the chapter for a planned Handbook of Mathematical
Methods in Imaging that surveys the mathematical models, problems, and
algorithms of the Thermoacoustic (TAT) and Photoacoustic (PAT) Tomography. TAT
and PAT represent probably the most developed of the several novel ``hybrid''
methods of medical imaging. These new modalities combine different physical
types of waves (electromagnetic and acoustic in case of TAT and PAT) in such a
way that the resolution and contrast of the resulting method are much higher
than those achievable using only acoustic or electromagnetic measurements.
