----------------------------------------------------------------------- `Fluxbranes: Moduli Stabilisation and Inflation' Abstract: Fluxbrane inflation is a realization of D-term hybrid inflation in string theory, featuring some appealing phenomenological characteristics. In contrast to other brane inflation models, fluxbrane inflation obtains naturally flat inflaton potential by compactifying on a manifold with large volume and thus does not rely on strong warping or heavy anisotropy in the compact space. In this talk, I will present the most interesting aspects of the model and discuss recent progress and new challenges regarding moduli stabilisation. -----------------------------------------------------------------------