  The Brownian web is a collection of one-dimensional coalescing Brownian
motions starting from everywhere in space and time, and the Brownian net is a
generalization that also allows branching. They appear in the diffusive scaling
limits of many one-dimensional interacting particle systems with branching and
coalescence. This article gives an introduction to the Brownian web and net,
and how they arise in the scaling limits of various one-dimensional models,
focusing mainly on coalescing random walks and random walks in i.i.d.
space-time random environments. We will also briefly survey models and results
connected to the Brownian web and net, including alternative topologies,
population genetic models, true self-repelling motion, planar aggregation,
drainage networks, oriented percolation, black noise and critical percolation.
Some open questions are discussed at the end.
