Future cluster surveys will produce catalogs of thousands of galaxy clusters and can place precise statistical constraints on cosmological parameters. I will discuss constraints in forthcoming surveys that will identify clusters by their X-ray emission, Sunyaev-Zeldovich decrement, or weak lensing shear. Each survey yields information on the abundance and the power spectrum of clusters. The combination of these observables helps breaking degeneracies between cosmological parameters, and to reduce systematic errors. In this talk, I will focus on two outstanding questions. First, cluster surveys can help achieve a sensitivity of dw/da ~ 0.1 on measurements of the evolution dw/da of the dark energy equation of state, and to distinguish between competing models for the dark energy. Second, cluster surveys can help achieve a sensitivity of ~0.05eV for the sum of the masses of neutrinos. This is the present-day lower limit from oscillations experiments, and would make a neutrino detection very likely.