  A twisted quiver bundle is a set of holomorphic vector bundles over a complex
manifold, labelled by the vertices of a quiver, linked by a set of morphisms
twisted by a fixed collection of holomorphic vector bundles, labelled by the
arrows. When the manifold is Kaelher, quiver bundles admit natural
gauge-theoretic equations, which unify many known equations for bundles with
extra structure. In this paper we prove a Hitchin--Kobayashi correspondence for
twisted quiver bundles over a compact Kaehler manifold, relating the existence
of solutions to the gauge equations to a stability criterion, and consider its
application to a number of situations related to Higgs bundles and dimensional
reductions of the Hermitian--Einstein equations.
