Current and future surveys of the cosmological density field are enabling the construction of large-than-ever catalogues of clusters and voids in the cosmological distribution of galaxies. The internal and cross-catalogue statistics, as well as object properties, in such samples are sensitive probes of fundamental physics: for example gravity, dark energy, and dark matter. Cross-comparison with data on gravitational lensing and peculiar velocities enable additional powerful tests. I will discuss recent developments in this field, and the prospects for testing fundamental physics using future large-scale surveys of clusters and voids with telescopes such as Euclid and the Square Kilometer Array.