The Lipschitz operators allow to establish an explicit connection between some non-linear dynamical systems and linear dynamical systems. A natural question then arises : how can we understand the dynamical properties of these operators from the properties of the associated nonlinear dynamical system? In this presentation, we will focus on the notion of hypercyclicity, which is based on the existence of dense orbits, and we will examine how certain criteria within the nonlinear context enable us to get hypercyclic Lipschitz operators.