I will introduce the ongoing research program, joint with Oliver Pechenik, Stephan Pfannerer, Jessica Striker, and Josh Swanson, in which we reinterpret webs as "hourglass plabic graphs" whose trip permutations align with the promotion permutations of tableaux. I will describe the application of this perspective to the construction of an SL(4) web basis generalizing Kuperberg's SL(3) basis, and, time permitting, will mention further applications to geometric embeddings of webs generalizing those of Fontaine-Kamnitzer-Kuperberg and to more general web bases.