The paper by Oded Schramm explores the scaling limits of loop-erased random walks (LERW) and uniform spanning trees (UST) in the plane. Despite the existence of scaling limits being unproven, the existence of subsequential scaling limits is established. Schramm proves that any LERW subsequential scaling limit is a simple path, and the trunk of any UST subsequential scaling limit is a topological tree dense in the plane. The paper also discusses the conformal invariance conjecture for LERW and provides a precise statement, showing that this conjecture implies an explicit construction of the scaling limit using Löwner's differential equation with Brownian motion. Additionally, the paper addresses the scaling limits of critical percolation and the Peano curve, and plans to explore these topics further in subsequent work.The paper by Oded Schramm explores the scaling limits of loop-erased random walks (LERW) and uniform spanning trees (UST) in the plane. Despite the existence of scaling limits being unproven, the existence of subsequential scaling limits is established. Schramm proves that any LERW subsequential scaling limit is a simple path, and the trunk of any UST subsequential scaling limit is a topological tree dense in the plane. The paper also discusses the conformal invariance conjecture for LERW and provides a precise statement, showing that this conjecture implies an explicit construction of the scaling limit using Löwner's differential equation with Brownian motion. Additionally, the paper addresses the scaling limits of critical percolation and the Peano curve, and plans to explore these topics further in subsequent work.