Exact calculations are performed on the two-dimensional strongly interacting, unpolarized, uniform Fermi gas with a zero-range attractive interaction. We describe recent advances in auxiliary-field quantum Monte Carlo techniques, which enable calculations on large enough lattices to reliably compute ground-state and finite temperature properties in the thermodynamic limit. An equation of state is obtained, which can serve as a benchmark and allow accurate comparisons with experiments. We show the spectral function, the density and spin structure factors from the state-of-art analytic continuation techniques, which provides unique tools to visualize the BEC-BCS crossover. The temperature effect of the equation of state, condensate fraction and pairing wave function will be discussed.