The authors report the experimental realization of the Haldane model on a honeycomb lattice using ultracold fermionic atoms. The model, which features topologically distinct phases of matter, is realized by breaking both time-reversal symmetry (TRS) and inversion symmetry (IS). TRS is broken through complex next-nearest-neighbour tunneling terms induced by circular modulation of the optical lattice, while IS is broken by an energy offset between neighboring sites. The band structure is probed using momentum-resolved interband transitions, and the Berry curvature of the lowest band is explored by applying a constant force to the atoms. The competition between broken symmetries gives rise to a transition between topologically distinct regimes, which is mapped out experimentally and compared to theoretical calculations. The approach is shown to be suitable for interacting fermionic systems and can be extended to realize spin-dependent topological Hamiltonians.The authors report the experimental realization of the Haldane model on a honeycomb lattice using ultracold fermionic atoms. The model, which features topologically distinct phases of matter, is realized by breaking both time-reversal symmetry (TRS) and inversion symmetry (IS). TRS is broken through complex next-nearest-neighbour tunneling terms induced by circular modulation of the optical lattice, while IS is broken by an energy offset between neighboring sites. The band structure is probed using momentum-resolved interband transitions, and the Berry curvature of the lowest band is explored by applying a constant force to the atoms. The competition between broken symmetries gives rise to a transition between topologically distinct regimes, which is mapped out experimentally and compared to theoretical calculations. The approach is shown to be suitable for interacting fermionic systems and can be extended to realize spin-dependent topological Hamiltonians.