In traditional tomographic methods, the same physical kind of radiation is used for penetrating the target and for measuring the response (e.g., X-rays in the standard CT, ultrasound in ultrasound tomography, etc.). A variety of new “hybrid” methods is being currently developed, which involve different types of waves. The purpose is to combine the advantages of each type, while alleviating their individual deficiencies. These new modalities usually require new analytic and numerical techniques. The lectures will start with a brief review of some novel hybrid methods and then will concentrate on the mathematical techniques and problems of the most developed hybrid modality, the so called thermoacoustic (or photoacoustic) imaging.