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© IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. LM and MR acknowledge fruitful discussions with U Schneider with whom the superlattice idea was actually conceived. We also thank J I Cirac, S Dürr, G Juzeliunas, W Phillips, I Spielman, and C Wu. LM and MR thank Caixa Manresa and ICFO for hospitality; MR and ML thank KITP for hospitality. MR and ML have received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 247687 (IP-AQUTE). ML also acknowledges financial support from ERC Grant QUAGATUA, EU STREP NAMEQUAM, MINCIN FIS2008-00784, the Alexander von Humbold Foundation and Hamburg Theory Award. NG thanks the FRS-FNRS for financial support. AB and MAMD thank MICINN FIS2009-10061, CAM QUITEMAD, European FET-7 PICC and UCM-BS GICC-910758., We present a proposal for a versatile cold-atom-based quantum simulator of relativistic fermionic theories and topological insulators in arbitrary dimensions. The setup consists of a spin-independent optical lattice that traps a collection of hyperfine states of the same alkaline atom, to which the different degrees of freedom of the field theory to be simulated are then mapped. We show that the combination of bi-chromatic optical lattices with Raman transitions can allow the engineering of a spin-dependent tunneling of the atoms between neighboring lattice sites. These assisted-hopping processes can be employed for the quantum simulation of various interesting models, ranging from noninteracting relativistic fermionic theories to topological insulators. We present a toolbox for the realization of different types of relativistic lattice fermions, which can then be exploited to synthesize a majority of phases in the periodic table of topological insulators., European Community’s Seventh Framework Programme (FP7/2007-2013), ERC, MINCIN, Alexander von Humbold Foundation, Hamburg Theory Award, FRS-FNRS, CAM, Spain, European FET-7 PICC, UCM-BS, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub