Abstract: The Derrida-Retaux model is a toy version of hierarchical renormalisation models in statistical physics. It brings in, in connection with the Derrida-Retaux conjecture, a number of very simple mathematical questions, most of which remain unanswered. I am going to make elementary discussions on some of the questions, and report work in progress with Xinxing Chen (Shanghai), Victor Dagard (Paris), Bernard Derrida (Paris), Yueyun Hu (Paris), Mikhail Lifshits (St. Petersburg).