This thesis describes a study of the clustering properties of galaxies and clusters of galaxies as measured by the power spectrum (P(k)) and the counts in cells statistic. The samples used are the optical Stromlo-APM galaxy survey, the APM cluster survey and the IRAS 1.2Jy, QDOT and PSCz surveys. Throughout, N-body simulations, for a variety of cosmological models, are used to test methods and to supplement analytic error estimates. For the Stromlo-APM sample the amplitude of the power spectrum is dependent on galaxy morphology. Early-type galaxies show a higher clustering amplitude than late-type galaxies by a factor of ~ 1.8. There is also tentative evidence for some dependence of the clustering amplitude on galaxy luminosity. The parameter Ω0.6/b is estimated via a comparison with the real-space power spectrum of the two-dimensional APM galaxy survey. For APM clusters the power spectrum is measured to very small wave numbers, with a possible detection of the expected turn-over. The results are inconsistent with the standard cold dark matter model. The shape of P( k) for clusters is approximately the same as that for Stromlo-APM galaxies but amplified by a factor of ~ 3.5. The power spectrum of the QDOT sample depends sensitively on the galaxy weighting scheme, probably due the manner in which the region of the Hercules supercluster is sampled. A best estimate of the power spectrum of IRAS galaxies is computed by combining the IRAS l.2Jy and QDOT samples. The PSCz galaxy power spectrum is also computed. The PSCz galaxies have a clustering amplitude twice that of optical galaxies. A similar result is found from a joint counts in cells analysis. Redshift-space distortions in the PSCz sample are analysed using a spherical harmonic decomposition of the density field. The value of Ω0.6/b = 1 is ruled out by this analysis at the 2σ significance level.