The combinatorial spider is a diagrammatic category that encodes quantum $\mathfrak{sl}_n$ representations, and was formalized by Kuperberg. Webs correspond to the morphisms in this category, drawn as directed planar graphs with skein-type relations that indicate algebraic equivalences. Webs are well-understood in the case $n=2$, when they are essentially the Temperley-Lieb diagrams, and in the substantially more complicated case $n=3$. But despite considerable interest from knot theorists, representation theorists, and combinatorists, we lacked a similar set of graph-theoretic tools to analyze webs explicitly when $n \geq 4$. In this talk, we sketch some of the historical evolution of webs, including work of Kuperberg, Khovanov, Fontaine, Cautis, Kamnitzer, Morrison, and others, as well as connections to algebraic geometry and combinatorics. We also describe a new approach using a set of colored paths called \emph{strands} that generalize graph-theoretic and combinatorial notions from smaller dimensions to $n \geq 4$, and that also give global information about webs. This work is joint with Heather M. Russell.