A methodology is presented for the generation and meshing of large-scale three-dimensional random polycrystals. Voronoi tessellations are used and are shown to include morphological properties that make them particularly challenging to mesh with high element quality. Original approaches are presented to solve these problems: (i) ''geometry regularization'', which consists in removing the geometrical details of the polycrystal morphology, (ii) ''multimeshing'' which consists in using simultaneously several meshing algorithms to optimize mesh quality, and (iii) remeshing, by which a new mesh is constructed over a deformed mesh and the state variables are transported, for large strain applications. Detailed statistical analyses are conducted on the polycrystal morphology and mesh quality. The results are mainly illustrated by the high-quality meshing of polycrystals with large number of grains (up to 10 5), and the finite element method simulation of a plane strain compression of e = 1.4 of a 3000-grain polycrystal. The presented algorithms are implemented and distributed in a free (open-source) software package: Neper.

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