A major aim of researchers working in the field of optics and photonics is to mold the flow of light in optical structures and devices. In the regime of ballistic light propagation, transformation optics has given a certain boost, for which optical invisibility cloaking devices are striking examples. Our capability to mold the flow of light in the regime of diffuse light propagation in light-scattering media has fallen behind—while diffuse light from clouds, white wallpaper, computer monitors, and lightemitting diodes is literally all around us every day. In this review, we summarize progress in steering the flow of diffuse light in turbid media which was triggered by the mathematical analogy between electrostatics, magnetostatics, stationary heat conduction, and stationary light diffusion. We give an extensive tutorial introduction to the mathematics of the diffusion equation for light and its solutions, present an overview on the current experimental state-of-the-art of simple core–shell invisibility cloaking, and compare these experiments with diffusion theory as well as with more advanced modelling based on Monte Carlo simulations. The latter approach enables spanning the bridge from diffusive to ballistic light propagation.