We investigate the polycrystalline microstructure, i.e. grain size and orientation distribution, that forms during laser crystallisation of amorphous silicon on glass substrates by a frequency doubled Nd:YVO4-laser operating at a wavelength of 532 nm. Transmission electron microscopy reveals that the grains have an average width from 0.25 to 3 mum and a length of several 10 mum. Electron back-scattering diffraction indicates that the grain orientation of the poly-Si films is textured. Type and extent of texturing depend in a complex way on the thickness of the crystallised amorphous silicon layer and on whether or not a buffer layer is present.