By Daniel Kious, NYU Shanghai

The Once-reinforced random walk was introduced in the nineties as an a priori simplistic model of random walk with memory. Since then, only a few results have been proved, but very interesting features have been conjectured, some of them related to the geometry of the range.
We will give an overview of the current knowledge on these questions, eventually focusing on a recent result of Vladas Sidoravicius and myself.