Integral geometry is dedicated to the study of transforms mapping a function defined on a manifold to its integrals over a family of submanifolds. Some typical examples of such transforms include the X-ray transform taking a function of n variables to its integrals over a family of all lines in R^n, the Radon transform taking a function of n variables to its integrals over all possible hyperplanes, the spherical Radon transform integrating a function over a family of spheres. The talk will discuss the Radon transform and its generalizations in relation to problems arising in some novel medical imaging modalities, such as thermo and photo-acoustic tomography.