Hubbard models describe the competition of tunnelling of a single fermion between neighboring sites, and a strong local interaction between two fermions. The corresponding Hamiltonian operators have been used to model a variety of physical phenomena, ranging from the Mott insulator to high Tc superconductivity. Very recently the Mott insulating state has been observed in ultracold gases of fermionic atoms confined onto optical lattices, opening the way to the use of these systems as quantum simulators of Hubbard models, and ultimately of the physics of real condensed matter materials. We discuss the zero temperature phase diagram of these Hamiltonians, with emphasis on the role of correlated hopping terms in the onset of quantum phase transitions.