  This is a review article exploring similarities between moduli of quiver
representations and moduli of vector bundles over a smooth projective curve.
After describing the basic properties of these moduli problems and
constructions of their moduli spaces via geometric invariant theory and
symplectic reduction, we introduce their hyperk\"ahler analogues: moduli spaces
of representations of a doubled quiver satisfying certain relations imposed by
a moment map and moduli spaces of Higgs bundles. Finally, we survey a
surprising link between the counts of absolutely indecomposable objects over
finite fields and the Betti cohomology of these (complex) hyperk\"ahler moduli
spaces due to work of Crawley-Boevey and Van den Bergh and Hausel, Letellier
and Rodriguez-Villegas in the quiver setting, and work of Schiffmann in the
bundle setting.
