The analysis of absorption systems in the spectra of high-z quasars has represented for several decades the only practical way to obtain information about the properties of the Intergalactic Medium (IGM). Unfortunately this information is almost always one-dimensional. An interesting alternative to absorption studies is to try to detect the IGM in emission rather than in absorption. Optically thick clouds to the cosmic ionizing background (or local ionizing sources, e.g. quasars) are expected to emit fluorescent Ly-alpha photons produced in hydrogen recombinations at a rate that is set by the impinging ionizing flux. In the first part of the talk, I will discuss how to model this emission and I will show recent observational results of a survey around a quasar at z~3. In the second part of the talk I will present a new method to directly map the cosmic neutral hydrogen during reionization with the Ly-alpha emission generated within the quasar Ionization fronts. I will show that the expected signal can be already detected with current facilities, shedding new light on the reionization epoch and the properties of the high-z quasars.