Galaxy clusters form from the rarest peaks in the initial matter distribution, and hence are a sensitive probe of the amplitude of density fluctuations (sigma_8), the amount of matter in the universe, and the growth rate of structure. Galaxy clusters have the potential to constrain dark energy and neutrino masses. However, cluster cosmology is currently limited by systematic uncertainties due to poorly understood intracluster gas physics. I will present new statistical approaches to understand clusters and improve their cosmological constraining power through the thermal Sunyaev-Zel'dovich (tSZ) effect. First, I will describe a forthcoming first detection of the cross-correlation of the tSZ signal reconstructed from Planck data with the large-scale matter distribution traced by the Planck CMB lensing potential. This statistic measures the amount of hot gas found in moderately massive groups and clusters (M ~ 10^13-10^14.5 M_sun), a mass scale below that probed by direct cluster detections. Second, I will describe the first measurement of the PDF of the tSZ field using ACT 148 GHz maps. This measurement contains information from all (zero-lag) moments of the tSZ field, beyond simply the 2- or 3-point functions. It is a very sensitive probe of sigma_8 and may also provide a method with which to break the degeneracy between sigma_8 and uncertainties in the physics of the intracluster gas.