Despite its global homogeneity and isotropy, the local matter distribution in the late Universe is manifestly inhomogeneous. Understanding the various effects resulting from these inhomogeneities is one of the most important tasks of modern cosmology. In this thesis, we investigate two aspects of the influence of local structure: firstly, to what extent do local structures modify the average expansion of spatial regions with a given size, and secondly, how strongly does the presence of structure limit the possible accuracy of measurements in our cosmic neighborhood.

To address these questions we first characterize the properties of the local inhomogeneities; we recall basic measures of fluctuations and go beyond them using the robust morphological tool of the Minkowski functionals. In particular, we apply these measures to the Sloan Digital Sky Survey data release seven. We find that the morphology of the luminous red galaxy data is marginally consistent with the one derived from simulations within the LCDM framework. In addition we illustrate, how the Minkowski functionals provide a description of clustering properties, and why this description goes beyond the standard two-point statistics. Minkowski functionals do therefore provide a measure for the amount of non-Gaussianity that we find in the galaxy data.

With this information on the amount of structure in the observed Universe, we choose to model these structures by employing the relativistic Zel'dovich approximation (RZA) to find out, whether they can affect the average evolution. To this end, we use the Buchert scheme of averaging and evaluate the magnitude of the kinematical backreaction term, which is one modification with respect to the equations without structure. The other modification is a change in evolution of the averaged curvature. We find that, within the RZA, kinematical backreaction affects only the evolution on small scales, while curvature may lead to effects on larger scales. More precisely, the contribution of backreaction to the cosmic energy budget, is larger than 1% below 100 Mpc only. We show that our results are consistent with the results obtained by other perturbative methods and also with those of a toy model that tries to capture non-perturbative effects.

The observation of a significant curvature contribution on scales larger than the homogeneity scale finally motivates the investigation of its effects on the accuracy of local measurements. We derive the fluctuations of the cosmological parameters in recent galaxy surveys, and find that domains as big as 540h^-1Mpc may still have a curvature contribution to the energy budget of 1%. This may limit our ability to measure the dark energy equation of state. We find that the Hubble rate today can never be directly measured with an accuracy better than 0.5%. Finally we show how backreaction and cosmic variance are linked to each other.