Abstract: Lipschitz trees form a very well-behaved subclass of Aronszajn trees under MA or PFA. In Todorcevic’s paper Lipschitz Maps on Trees, he proved that MA implies every two Lipschitz trees are comparable. Todorcevic also de…ned an ultra…lter for Lipschitz tree and proved under MA that two Lipschitz trees are equivalent if and only if they have the same ultra…lter. I will present selected results from that paper as well as my attempt to generalize Lipschitz trees to $\omega_2$.