We offer here a brief introduction to the idea of quantum simulations with cold atomic gases, with focus on the recent efforts towards artificial gauge potentials and fields.This is mainly intended as a sort of "pedestrian guide" for people not yet working in the field, but curious to get a first contact with it; longer and deeper reviews are addressed for deeper details.As a special case, we focus here on reviewing some own previous contributions about a flexible toolbox based on bichromatic optical lattices and Raman assisted tunnelling.Such a scheme would allow good control on the mass and kinetic terms of a lattice Hamiltonian in different effective dimensions.If realized with fermionic atoms, the low-energy sector effectively describes their relativistic dynamics in a variety of situations, among which 3D axion electrodynamics.We conclude with a short discussion of possible future directions. QCD-TNT-III-From quarks and gluons tohadronic matter: A bridge too far?, 2-6 September, 2013 European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Villazzano, Trento (Italy) * Speaker.