  We discuss the projectivity of the moduli space of semistable vector bundles
on a curve of genus $g\geq 2$. This is a classical result from the 1960s,
obtained using geometric invariant theory. We outline a modern approach that
combines the recent machinery of good moduli spaces with determinantal line
bundle techniques. The crucial step producing an ample line bundle follows an
argument by Faltings with improvements by Esteves-Popa. We hope to promote this
approach as a blueprint for other projectivity arguments.
