Saharon Shelah proved a remarkable theorem of cardinal arithmetic in 1989: if $\aleph_\omega$ is a strong limit cardinal, then $2^{\aleph_\omega}<\aleph_{\omega_4}$. His proof used the tools of pcf theory (a body of set-theoretic tools that are helpful in analyzing certain types of infinite products) but it was soon realized that once the basic ingredients of pcf theory are given, the rest of the argument is essentially topological. Our aim is to survey the topological aspects Shelah’s proof, and present some recent applications.