This paper introduces a class of smooth projective varieties that generalize and share many properties with partial flag varieties of type $A$ . The quiver flag variety $\mathcal{M}_\vartheta(Q,\underline{r})$ of a finite acyclic quiver $Q$ (with a unique source) and a dimension vector $\underline{r}$ is a fine moduli space of stable representations of $Q$ . Quiver flag varieties are Mori dream spaces, they are obtained via a tower of Grassmann bundles, and their bounded derived category of coherent sheaves is generated by a tilting bundle. We define the multigraded linear series of a weakly exceptional sequence of locally free sheaves $\underline{\mathscr{E}} = (\mathscr{O}_X,\mathscr{E}_1,\dots, \mathscr{E}_\rho)$ on a projective scheme $X$ to be the quiver flag variety $\vert \underline{\mathscr{E}}\vert:=\mathcal{M}_\vartheta(Q,\underline{r})$ of a pair $(Q, \underline{r})$ encoded by $\underline{\mathscr{E}}$ . When each $\mathscr{E}_i$ is globally generated, we obtain a morphism $\varphi_{\vert \underline{\mathscr{E}}\vert}\colon X\to \vert \underline{\mathscr{E}}\vert$ , realizing each $\mathscr{E}_i$ as the pullback of a tautological bundle. As an application, we introduce the multigraded Plücker embedding of a quiver flag variety.