In the context of hybrid medical imaging methods, coupling ultrasonic waves with electrical impedance imaging leads in certain contexts to an inverse conductivity problem with internal data functionals of "power density" type. After presenting how to derive such a problem, we will review inversion techniques that were obtained in the past few years for this problem, first in the isotropic case, and if time allows, in the anisotropic case. In both cases, if a "rich enough" set of functionals is provided, all of the conductivity tensor is uniquely reconstructible with good stability properties. This will be contrasted with the results available when considering the same problem from boundary measurements (i.e. Calderon's problem).