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This paper is the second part of our survey of results on universality for cellular automata in the hyperbolic plane and in the hyperbolic 3D-space. Here we remind the notion of universality and its variants. We also remind the railway model on which many of our results are based for universal cellular autmata in the hyperbolic plane and in the hyperbolic 3D space. We conclude this section with a application to the pentagrid, the heptagrid, the dodecagrid and the tessellation {11, 3} of the hyperbolic plane. [ABSTRACT FROM AUTHOR]