We will introduce the skew Brownian motion as a perturbation of the standard Brownian motion and give a brief insight on the local time process and its corresponding excursion process. We will then review some connections of the skew Brownian motion with various other fields of research in applied probability theory such as the stochastic interpretation of divergence form operators, the study of the local time flow and the possible construction of spider processes. Even tough some issues might be perceived as technical, an effort will be made so that the talk may be well attended by non-specialists.