Embarking on an exploration of high-dimensional lattice models, this presentation delves into contemporary advancements within the realm of percolation, self-avoiding walks, the Ising model, and the XY model. Our approach diverges from traditional lace-expansion and renormalization techniques, opting for an innovative perspective that elucidates mean-field behavior. The crux of our methodology lies in an examination of the random-walk representation inherent in these intricate models.