Free Electron Lasers (FEL) are commonly regarded as the potential key application of laser wakefield accelerators (LWFA). It has been found that electron bunches exiting from state-of-the-art LWFAs exhibit a normalized 6-dimensional beam brightness comparable to those in conventional linear accelerators. Effectively exploiting this beneficial beam property for LWFA-based FELs is challenging due to the extreme initial conditions particularly in terms of beam divergence and energy spread. Several different approaches for capturing, reshaping and matching LWFA beams to suited undulators, such as bunch decompression or transverse-gradient undulator schemes, are currently being explored. In this article the transverse gradient undulator concept will be discussed with a focus on recent experimental achievements.
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