The progression of a liquid inside a porous medium often involves two macroscopic fronts: a main one, at the bottom, which saturates the medium; and a much thinner one, ahead, which propagates using the fine structures of the porous material. We discuss here different characteristics of this precursor. We show in particular how it can move faster than the main front, although it follows confined paths. We also describe its dynamics, and compare our results with different experimental situations.