Weyl semimetals are 3d topological materials that show, upon breaking time-reversal or inversion symmetry, couples of gap-closing points with opposite topological "charges". Around these points, the system is effectively described by a massless fermion's Weyl equation, with the role of topological charge played by chirality. Weyl points are robust against perturbations and symmetry breaking: applying a perturbation that slightly changes the Hamiltonian, they can be shifted in the Brillouin zone and can only be destroyed by annihilation, making points of opposite charge coincide. If the system breaks translational invariance, e.g. is finite in one direction, peculiar zero-energy surface states known as Fermi arcs appear, connecting the projections on the cut surface of Weyl points of opposite chirality. Weyl semimetals are obtainable in many different systems: in our case, first we consider a cubic optical lattice, engineered with laser-assisted tunnelling to break inversion symmetry so to realize a special case of Harper model, and study the evolution of Weyl point projections and Fermi arcs upon varying the sublattice energy offset and the direction of the cut surface. We also observe the associated real-space propagation of a gaussian wavepacket on the surface of a chunk of material. Weyl semimetals can also be realized in correlated electron systems: to this end we consider a 3d fermionic lattice model with two bands near the Fermi energy, such as the BHZ model or a simple 3d topological insulator with spin-orbit coupling. We then add a time-reversal or inversion symmetry breaking perturbation and study the topological character of the system upon varying the effective mass and Hubbard U parameter. We observe the topological phase transition the system undergoes passing from a orbital-polarized unmagnetized region to an orbital-unpolarized magnetized one. The study is done both via mean-field approximation (Hartree-Fock) and via DMFT.