The aim of this cosmology proposal is to study the contents, history and evolution of our Universe, using the distribution of matter on large scales. I propose to study new methods to identify and catalogue rare voids and superclusters in the large-scale structure of the Universe and to study their statistical, morphological and dynamical properties. I will use these studies to propose new observables and new techniques of data analysis based on these structures, and to use this knowledge to test theories of gravitation, dark energy and the initial conditions of the early Universe. Interest in cosmic voids in particular has increased greatly in recent years, as they have been suggested as extremely competitive probes of cosmology, according to some estimates significantly out-performing other methods. Yet there remain unsolved theoretical difficulties in the modelling of voids and even a lack of consensus on how to identify them and how to relate theory and observation. Even less is currently known about superclusters. These are among the important issues I propose to address. My proposal consists in roughly equal parts of: analysis of the latest high-quality survey data which will available from the Sloan Digital Sky Survey (SDSS) and the Dark Energy Survey (DES); analysis of the state-of-the-art Jubilee ISW and weak lensing simulations run on the Juropa supercomputer in Germany; and theoretical work to combine insights from data and simulation to improve our understanding of cosmology. The proposed work is to be carried out in collaboration with leading experts in the respective fields from across the European Community, in particular in the United Kingdom, Spain and Germany.