The large-scale structure of the Universe is delineated by the spatial distributions of galaxies and clusters of galaxies. This thesis describes three projects concerned with the use of galaxies and clusters as cosmological probes, following the presentation of necessary background material in Chapter 1. Chapter 2 is concerned with spatial correlations of clusters of galaxies. After comprehensively reviewing previous work addressing this topic from both observational and theoretical points of view, we present, test and apply an important new method for computing theoretical cluster correlations. Our method combines the theory of peaks in Gaussian random fields with the evolution of the cosmological density field by the Zeldovich Approximation: this is the first analytic calculation of the cluster correlation function to take account of the nonlinear evolution of the cosmological density field on cluster scales. We find good agreement between our results and those from recent numerical simulations, except for the richest cluster samples, for which our method yields stronger clustering. Comparison of our predicted correlations with those observed in recent optical cluster samples reveal that the once-popular Einstein - de Sitter Cold Dark Matter (CDM) model lacks the large-scale power required to match the observed clustering. We also apply our method in the first theoretical study of the spatial correlations of ROSAT clusters. Our results here favour cosmogonies with more large-scale power than CDM, in accordance with those we obtained from optical cluster samples. The projects in Chapters 3 and 4 are concerned with galaxy clustering.